System and method of monitoring, predicting and optimizing production yields in a liquid crystal display (LCD) manufacturing process

ABSTRACT

A system and method of monitoring LCD production yields, predicting the effects of different testing methodologies on LCD production yields, and optimizing production yields is provided that compares the effect of different testing methodologies on the yields at various stages in the LCD testing and assembly process. The present invention can also be used to predict the effect of different testing methodologies on user-defined parameters, such as profit.

This is a continuation of U.S. patent application Ser. No. 10/355,059filed Jan. 31, 2003 now U.S. Pat. No. 6,862,489.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to LCD manufacturing and, more particularly, to asystem and method of monitoring LCD production yields, predicting theeffects of different testing methodologies on LCD production yields, andoptimizing production yields.

2. Background of the Related Art

Yield management is important in LCD manufacturing. In LCDmanufacturing, a single large plate of glass is divided into just ahandful of LCD panels. As consumer demand grows for larger and largerdisplays, substrates get larger and the number of LCD panels per glassplate decreases. Accordingly, production yields are critical in LCDmanufacturing.

The majority of the costs of an LCD panel comes from manufacturing. As aresult, profitability is closely linked to yield rates. Any changes inyield rates will have a financial impact.

LCD panel production is a highly automated process involving variousmanufacturing stages. Each manufacturing stage consists of many complexsteps. For example, one stage of the process creates the thin-filmtransistor arrays on the glass substrate, which includes multiple passesof thin film deposition, resist layers, exposure, development, etchingand stripping. The opportunities for defects occur at nearly every stepof every stage in the manufacturing process.

Defects take several different forms, and can generally be divided intooptical, mechanical and electrical defects. Some of these defects can berepaired, while others are permanent and may be severe enough to renderthe LCD panel unusable.

Optical defects are the most common defect. When this type of defect ispresent, a pixel is “stuck” in either a bright state, in which the pixelalways transmits light, or a dark state, in which the pixel nevertransmits light. The most common cause for this type of defect is anelectrical problem, such as a short or an open circuit in the cell'stransistor or signal leads. Light or dark spots can also be caused byforeign particle contamination between the glass plates, or between theLCD panel and the backlight.

Another type of optical defect is non-uniformity, which can be caused bynon-uniform cell gaps that result in varying thickness of the liquidcrystal layer. Uniformity problems can also be caused by errors in therubbing process for liquid crystal alignment layers, inconsistent colorfilter thickness or incomplete removal of chemical residues.

Mechanical defects can include broken glass and broken electricalconnections. Broken electrical connections can arise from improperassembly, errors in alignment of the components and/or mishandling.

Some LCD manufacturers use testing and inspection equipment that canautomatically evaluate panels at intermediate points in themanufacturing process. In some cases, the defects can be automaticallyrepaired. However, comprehensive testing in the LCD production processslows down production. In addition, there are capital and maintenancecosts associated with the test equipment. Accordingly, manufacturershave to balance the need for comprehensive and accurate testing againstthe need to avoid slowing production as much as possible.

SUMMARY OF THE INVENTION

An object of the invention is to solve at least the above problemsand/or disadvantages and to provide at least the advantages describedhereinafter.

To achieve the objects, and in accordance with the purpose of theinvention, as embodied and broadly described herein, the presentinvention provides a system and method of monitoring LCD productionyields, predicting the effects of different testing methodologies on LCDproduction yields, and optimizing production yields by comparing theeffect of different testing methodologies on the yield at various stagesin the LCD testing and assembly process. The present invention can alsobe used to predict the effect of different testing methodologies onuser-defined parameters, such as profit.

In a preferred embodiment, the different testing methodologies areevaluated using a common production run. This reduces the number of LCDpanels required to test the different methodologies, and also reducesthe probability of LCD panels being sacrificed when an improper testingmethodology is applied.

Additional advantages, objects, and features of the invention will beset forth in part in the description which follows and in part willbecome apparent to those having ordinary skill in the art uponexamination of the following or may be learned from practice of theinvention. The objects and advantages of the invention may be realizedand attained as particularly pointed out in the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described in detail with reference to thefollowing drawings in which like reference numerals refer to likeelements wherein:

FIG. 1A is a block diagram of the process flow for TFT-LCD fabrication,in accordance with the present invention;

FIG. 1B is a block diagram of one preferred embodiment of the processorof FIG. 1A;

FIG. 2 is a block diagram of the assembly stage 200 of the process flowshown in FIG. 1;

FIG. 3 is a plot showing the pixel voltage distribution when half of thepixels of the TFT-array panel have positive pixel voltages and the otherhalf have negative pixel voltages, in accordance with the presentinvention;

FIG. 4 is a block diagram showing the layout of a typical glasssubstrate 400 used in TFT-LCD manufacturing;

FIG. 5 is a flow chart of a method of generating the distributionfunctions for normal pixels and defective pixels in an actual productionenvironment, in accordance with the present invention;

FIG. 6 is a defect sorting table, in accordance with the presentinvention;

FIG. 7 is a flow chart of a process for sorting defective pixelsdiscovered using the results of the array test stage, array repairstage, cell inspection stage and module inspection stage, in accordancewith the present invention;

FIG. 8 is a revised defect sorting table for primary-test-only at theTFT-array test stage, in accordance with the present invention;

FIG. 9 is a revised defect sorting table for new-test-only at theTFT-array test stage, in accordance with the present invention;

FIG. 10 is a flow chart of a process for profit maximization for theTFT-LCD production line can be achieved by optimization of thethresholding parameters, in accordance with the present invention;

FIG. 11 is a flow chart of a process for initial defect sorting, inaccordance with the present invention;

FIG. 12 is a flow chart of a process for defect resorting for new screenthresholding, in accordance with the present invention;

FIGS. 13A-13D illustrate a flow chart of a process for profitmaximization of new and primary test recipes, in accordance with thepresent invention;

FIG. 14 is a defect sorting table for tighter new thresholdingparameters for a new test recipe, in accordance with the presentinvention;

FIG. 15 is a defect sorting table for looser new thresholding parametersfor a new test recipe, in accordance with the present invention;

FIG. 16 is a revised defect sorting table, in conjunction with theinitial defect sorting of FIG. 11, for primary-test-only at theTFT-array test stage, in accordance with the present invention;

FIG. 17 is a plot showing an example of the distribution of normal anddefective pixel voltages of a TFT-array panel, in accordance with thepresent invention;

FIG. 18 is a plot showing the over-killed and under-killed defects asthe threshold parameters are scanned, in accordance with the presentinvention;

FIG. 19 is a plot showing the differential effect of changing thresholdparameters for under-killed defects, in accordance with the presentinvention;

FIG. 20 is a plot showing the differential effect of changing thresholdparameters on over-killed defects, in accordance with the presentinvention;

FIG. 21 is a plot showing the differential effect of changing thresholdparameters on cell and module yields, in accordance with the presentinvention;

FIG. 22 is a plot showing the differential effect of changing thresholdparameters on total monetary benefit, in accordance with the presentinvention;

FIG. 23 is a plot showing the under-killed defects for different defectdensity values, in accordance with the present invention;

FIG. 24 is a plot showing the differential effect of changing thresholdparameters on the total monetary benefit, in accordance with the presentinvention; and

FIG. 25 is a plot showing how the profit improvement increases withincreasing defect density, in accordance with the present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

I. Thin-Film Transistor (TFT) Liquid Crystal Display (LCD) Fabrication

FIG. 1A is a block diagram of the process flow for TFT-LCD fabrication.The fabrication process can be divided into two stages, an array panelfabrication stage 100, in which the thin-film transistor (TFT) arraypanels are fabricated on a substrate, and a test and assembly stage 200,in which the TFT array panels are tested and the displays are assembled.

In the array panel fabrication stage, the glass substrate on which theTFT array panels are fabricated is cleaned at step 102. Steps 104-110represent well known process steps for forming TFT array panels on aglass substrate. They consist of a thin film deposition step 104, aphotoresist patterning step 106, and etching step 108 and a photoresiststripping and cleaning step 110. Steps 104-110 are repeated for eachpatterned thin film layer that is deposited on the glass substrate.

Multiple TFT array panels are typically fabricated on each glasssubstrate, which are also referred to as TFT-array base plates. Adisplay unit, such as an LCD display, utilizes one TFT array panel.

Once the TFT array panels are fabricated on the glass substrate, the TFTarray panels proceed to the test and assembly stage 200, during whichthe TFT array panels are tested, the liquid crystal (LC) cells areassembled and separated, and the electrical connections are made to theliquid crystal cells to yield the liquid crystal modules that willultimately be used in the LCDs. The assembly stage consists of varioussubstages, including an array test stage 202, an array repair stage 204,a cell assembly stage 206, a cell inspection stage 208, a moduleassembly stage 210 and a module inspection stage 212. The assembly stage200 may also optionally include a cell repair stage 214 and a modulerepair stage 216.

In the array test stage 202, each TFT array panel is tested by drivingthe panel with a test signal, which will be explained in more detailbelow. TFT array panels that are determined to be bad (e.g., defective)are sent to the array repair stage 204. The panels that are determinedto be good are sent to the cell assembly stage 206. In the array repairstage 204, the bad panels that can be repaired are repaired usingtechniques known in the art, and the repaired panels are then sent tothe cell assembly stage 206.

In the cell assembly stage 206, the LC cells are assembled by laminatingfront and rear glass plates to the TFT array panels and injecting liquidcrystal material between the front and rear glass plates usingtechniques known in the art. In addition, the individual LC cells areseparated from each other at this stage by dicing the TFT array baseplate (glass substrate).

The assembled and separated LC cells are then sent to the cellinspection stage 208, where they are inspected for defects. LC cellsthat are determined to be damaged can be sent to an optional cell repairstage 214. The LC cells that are determined to be good LC cells, and therepaired LC cells, if the optional cell repair stage 214 is implemented,are then sent to the module assembly stage 210.

In the module assembly stage 210, the required electrical connectionsare made to the LC cells to yield the LCD modules that will ultimatelybe used in LCDs. The LCD modules then proceed to the module inspectionstage 212, where they are tested using techniques known in the art. Anoptional module repair stage 216 can be used to repair LCD modules thatare deemed to be defective at the module inspection stage 212.

A processor 220 sends and receives data to/from the test and assemblystage 200. In a preferred embodiment, shown in FIG. 1B, the processor220 includes a comparison unit 222 and an estimating unit 224. Thecomparison unit 222 compares the inputs and outputs of the varioussubstages in the test and assembly stage 200 for different manufacturingsetups. The estimating unit 224 receives comparison data from thecomparison unit 222, and estimates the effect that a change in themanufacturing setup has on a desired parameter, such as profit. Theestimating unit 224 utilizes methodologies that will be described below.The estimate data produced by the estimating unit 224 may be used tooptimize the manufacturing setup used by the test and assembly stage200.

The processor 220 of the present invention is preferably implemented ona server may be implemented on a programmed general purpose computer, aspecial purpose computer, a programmed microprocessor or microcontrollerand peripheral integrated circuit elements, an ASIC or other integratedcircuit, a hardwired electronic or logic circuit such as a discreteelement circuit, a programmable logic device such as a FPGA, PLD, PLA,or PAL, or the like. In general, any device on which a finite statemachine capable of implementing the process steps and routines discussedbelow can be used to implement the processor 220.

II. Profit Model for TFT-LCD Fabrication

A profit model for TFT-LCD fabrication, in accordance with oneembodiment of the present invention, will be described with reference toFIG. 2, which is a block diagram of the assembly stage 200 of theprocess flow shown in FIG. 1.

The variables used to describe the main process stages of FIG. 2 aredefined as follows:

-   I_(A)=Number of input panels to array test stage 202;-   I_(AR)=Number of input panels to array repair stage 204;-   I_(C)=Number of input panels to cell inspection stage 208;-   I_(M)=Number of input panels to module inspection stage 212;-   O_(ATG)=Number of passed panels at array test stage 202;-   O_(ATB)=Number of irreparably bad panels at array test stage 202;-   O_(ATR)=Number of reparable panels at array test stage 202, which is    the same as I_(AR);-   O_(ARG)=Number of passed panels at array repair stage 204;-   O_(ARB)=Number of bad panels at array repair stage 204;-   O_(CG)=Number of passed panels at cell inspection stage 208;-   O_(CB)=Number of irreparably bad panels at cell inspection stage    208;-   O_(MG)=Number of passed panels at module inspection stage 212; and-   O_(MB)=Number of irreparably bad panels at module inspection stage    212.

For the optional production flow stages 214 and 216, the additionalvariables used are defined as follows:

-   O_(CIR)=Number of reparable panels at cell inspection stage 208;-   O_(MIR)=Number of reparable panels at module inspection stage 212;-   O_(CRG)=Number of passed panels at cell repair stage 214;-   O_(MRG)=Number of passed panels at module repair stage 216;-   O_(CRB)=Number of bad panels at cell repair stage 214; and-   O_(MRB)=Number of bad panels at module repair stage 216.

A model that describes the relationship between profits and variationsin yields at cell and module inspections will now be described. Certaincost variables will be used as follows:

-   C_(A)=Cost to make a TFT panel;-   C_(T)=Cost to test a TFT panel;-   C_(R)=Cost to repair a TFT panel;-   C_(C)=Cost of cell assembly for a TFT panel;-   C_(CI)=Cost of cell inspection for a TFT panel;-   C_(M)=Cost of module assembly for a TFT panel; and-   C_(MI)=Cost of module inspection for a TFT panel.

In order to have an initial reference for the evaluation of changes inthe manufacturing parameters used in the testing, inspection, orassembly stages, a current manufacturing setup is called a “primarymanufacturing setup”, and the results obtained with the primarymanufacturing setup are referred to as “primary results.”

The cost analysis is done in connection with the assembly stage 200 ofthe process flow, without the optional cell repair stage 214 and modulerepair stage 216. This assumes that there is no difference in costs andoutput quantities between the primary manufacturing setup and a proposednew manufacturing setup. The cost to manufacture a TFT-LCD panel usingthe primary setup, COST_(PRIME), can be expressed as follows:COST_(PRIME)=Array manufacturing cost+Array test cost+Array repaircost+Cell assembly cost+Cell inspection cost+Module assembly cost+Moduleinspection cost.  (1)

One can obtain the expressions for the cost values as follows:Array manufacturing cost=I_(A)C_(A)  (2)Array test cost=I_(A)C_(T)  (3)Array repair cost=I_(AR)C_(T)  (4)Cell assembly cost=I_(C)C_(C)  (5) Cell inspection cost=I_(C)C_(CI)  (6)Module assembly cost=I_(M)C_(M)  (7)Module inspection cost=I_(M)C_(MI)  (8)

The yields at each stage are defined as follows:Yield of array test (Y _(AT))=O _(ATG) /I _(A)  (9)Yield of array repair (Y _(AR))=O _(ARG) /I _(AR)  (10)Yield of cell inspection (Y _(C))=O _(CG) /I _(C)  (11)Yield of module inspection (Y _(M))=O _(MG) /I _(M)  (12)

Since I_(M)=O_(CG) without the optional cell repair and module repairstages 214 and 216, Equation (11) can be written as:I_(M)=Y_(C)I_(C)  (13)From Equations (1), (2)-(8), and (13) one obtains:COST_(PRIME) =I _(A) C _(A) +I _(A) C _(T) +I _(AR) C _(R) +I _(C) C_(C) +I _(C) C _(CI) +Y _(C) I _(C) C _(M) +Y _(C) I _(C) C _(MI)  (14)

The value of the final TFT-LCD module output, in the case of the primarymanufacturing setup without the optional cell repair and module repairstages 214 and 216, can be expressed as follows:PRODUCT_(PRIME) =O _(MG) P _(VALUE),  (15)where P_(VALUE) is the value of a TFT-LCD module fabricated using theprimary manufacturing setup. From Equations (12), (13), and (14), oneobtains:PRODUCT_(PRIME)=Y_(M)Y_(C)I_(C)P_(VALUE)  (16)

When a new manufacturing setup is used in the array test stage 202, cellinspection stage 206, module inspection stage 212, cell assembly stage206, and/or module assembly stage 210, one can expect to have new valuesrepresented by the following variables:

-   I′_(AR)=New number of input panels to array repair;-   I′_(C)=New number of input panels to cell inspection;-   I′_(M)=New number of input panels to module inspection;-   O′_(ATG)=New number of passed panels at array test;-   O′_(ATB)=New number of irreparably bad panels at array test;-   O′_(ATR)=New number of reparable panels at array test, which is the    same as I′_(AR);-   O′_(ARG)=New number of passed panels at array repair;-   O′_(ARB)=New number of bad panels at array repair;-   O′_(CG)=New number of passed panels at cell inspection, which is    same as I′_(M);-   O′_(CB)=Number of bad panels at cell inspection;-   O′_(MG)=New number of passed panels at module inspection;-   O′_(MB)=New number of bad panels at module inspection;-   Y′_(AT)=New yield of array test;-   Y′_(AR)=New yield of array repair;-   Y′_(C)=New yield of cell inspection; and-   Y′_(M)=New yield of module inspection.

One can then obtain a new set of expressions for the new manufacturingsetup, without the optional cell repair and module repair stages 214 and216, as follows:COST_(NEW) =I _(A) C _(A) +I _(A) C _(T) +I′ _(AR) C _(R) +I′ _(C) C_(C) +I′ _(C) C _(CI) +Y′ _(C) I′ _(C) C _(M) +Y′ _(C) I′ _(C) C_(MI)  (17)PRODUCT_(NEW)=Y′_(M)Y′_(C)I′_(C)P′_(VALUE),  (18)where P′_(VALUE) is the value of the TFT-LCD module fabricated with thenew manufacturing setup.

The profit increase (or deficit decrease), P, that results from the newmanufacturing setup is obtained as follows:P=COST_(PRIME)−COST_(NEW)+PRODUCT_(NEW)−PRODUCT_(PRIME)  (19)

From Equations (14), (16), (17), (18), and (19) one obtains thefollowing expression for P:P=(I _(AR) −I′ _(AR))C _(R)+(I _(C) −I′ _(C))C _(C)+(I _(C) −I′ _(C))C_(CI) +Y _(C) I _(C) C _(M) +Y _(C) I _(C) C _(MI) −Y′_(C) I′ _(C) C _(M) −Y′ _(C) I′ _(C) C _(MI) +Y′ _(M) Y′ _(C) I′ _(C)P′ _(VALUE) −Y _(M) Y _(C) I _(C) P _(VALUE)  (20)

During regular production of a TFT-LCD, one can assume thatO_(ATB)+O_(ARB)≅O′_(ATB)+O′_(ARB), because a bad panel usually getscarried to the next process stage, as the individual panels have not yetbeen separated from each other and are all on a common TFT-array baseplate. If this assumption is valid, then withI _(C) =I _(A)−(O _(ATB) +O _(ARB)), and  (21)I′ _(C) =I _(A)−(O′ _(ATB) +O′ _(ARB)),  (22)one obtains:I_(C)≅I′_(C)  (23)

Using Equation (23) in Equation (20), one obtainsP≅(I _(AR) −I′ _(AR))C _(R)+(Y _(C) −Y′ _(C))I _(C)(C _(M) +C _(MI))+(Y′_(M) Y′ _(C) P′ _(VALUE) −Y _(M) Y _(C) P _(VALUE))I _(C)  (24)Since the value of a TFT-LCD module is irrelevant to the manufacturingsetup, one obtains:P_(VALUE)=P′_(VALUE)  (25)

Thus, with Equation (25), Equation (24) can be further simplified as:P≅(I _(AR) −I′ _(AR))C _(R)+(Y _(C) −Y′ _(C))I _(C)(C _(M) +C _(MI))+(Y′_(M) Y′ _(C) −Y _(M) Y _(C))P _(VALUE) I _(C)  (26)Accordingly, Equation (26) can be used to calculate the profit increaseor decrease as a result of the yield variation that occurs due to a newmanufacturing setup.

One can use the relationships described above to evaluate the profitsand the production quantities needed to achieve a break-even point inTFT-LCD manufacturing. This type of cost analysis is done based on theassumption that no TFT array panels are discarded as bad panels duringTFT array process. The cost of TFT-LCD panel (COST) can be expressed asfollows:COST=Array manufacturing cost+Array test cost+Array repair cost+Cellassembly cost+Cell inspection cost+Module assembly cost+Moduleinspection cost+Packaging cost+Storage and transportation cost+Otherfixed cost.  (27)

One can obtain additional expressions for the cost values as follows:Packaging cost=I_(M)C_(P); and  (28)Storage and transportation cost=I_(M)C_(S),  (29)where C_(P) and C_(S) are the unit packaging and storage/transportationcost, respectively.

From Equations (2)-(8), (13), (27), (28), and (29) one obtains:COST=I _(A) C _(A) +I _(A) C _(T) +I _(AR) C _(R) +I _(C) C _(C) +I _(C)C _(CI) +Y _(C) I _(C)(C _(M) +C _(MI) +C _(P) +C _(S))+C _(F),  (30)where C_(F) is other fixed costs. The value of the final output, withoutthe optional cell and module repair stages 214 and 216, can be expressedas follows:PRODUCT=O_(MG)D_(SALE),  (31)where D_(SALE) is the sales price of a TFT-LCD product unit.

From Equations (12), (13), and (31), one obtains:PRODUCT=Y_(M)Y_(C)I_(C)D_(SALE).  (32)Then, the profit (PT) is obtained by:PT=PRODUCT−COST.  (33)

From Equations (30), (32), and (33), one obtains:PT=Y _(M) Y _(C) I _(C) D _(SALE)−(I _(A) C _(A) +I _(A) C _(T) +I _(AR)C _(R) +I _(C) C _(C) +I _(C) C _(CI) +Y _(C) I _(C)(C_(M) +C _(MI) +C_(P) +C _(S))+C_(F)).  (34)

Using Equation (21) in Equation (34), one obtains:PT=Y _(M) Y _(C)(I _(A) −O _(ATB) −O _(ARB))D _(SALE)−(I _(A) C _(A) +I_(A) C _(T) +I _(AR) C _(R) +C _(F)+(I _(A) −O _(ATB) −O _(ARB))(C _(C)+C _(CI) +Y _(C) C _(M) +Y _(C) C _(MI) +Y _(C) C _(P) +Y _(C) C_(S))).  (35)

If one defines Y_(T) as:Y _(T)≅(O _(ATB) +O _(ARB))/I _(A),  (36)then Equation (35) becomes:PT=Y _(M) Y _(C) I _(A)(1−Y _(T))D _(SALE)−(I _(A)(C _(A) +C _(T))+I_(AR) C _(R) +C _(F) +I _(A)(1−Y _(T))(C _(C) +C _(CI) +Y _(C)(C _(M) +C_(MI) +C _(P) +C _(S)))).  (37)

I_(A) for the break-even point where PT is zero (I_(A-EVEN)) becomes:I _(A-EVEN)=(I _(AR) C _(R) +C _(F))/(Y _(M) Y _(C)(1−Y _(T))D_(SALE)−(C _(A) +C _(T)+(1−Y _(T))(C _(C) +C _(CI) +Y _(C)(C _(M) +C_(MI) +C _(P) +C _(S))))).  (38)

In normal production, one can assume:O_(ATB)<<I_(A)  (39)Thus, with Equation (9), one obtains:I _(AR) =O _(ATR) =I _(A) −O _(ATB) −O _(ATG) ≅I _(A) −O _(ATG) =I_(A)(1−Y _(AT)).  (40)

From Equations (37) and (40), one obtains:

 PT≅Y _(M) Y _(C) I _(A)(1−Y _(T))D _(SALE)−(C _(F) +I _(A)(C _(A) +C_(T)+(1−Y _(AT))C _(R)+(1−Y _(T))(C _(C) +C _(CI) +Y _(C)(C _(M) +C_(MI) +C _(P) +C _(S))))).  (41)

I_(A-EVEN) is again obtained for I_(A), making PT=0 in Equation (41), asfollows:I _(A-EVEN) ≅C _(F)/(Y _(M) Y _(C)(1−Y _(T))D _(SALE)−(C _(A) +C_(T)+(1−Y _(AT))C _(R)+(1−Y _(T))(C _(C) +C _(CI) +Y _(C)(C _(M) +C_(MI) +C _(P) +C _(S))))).  (42)Accordingly, the profit and the production quantities needed forbreak-even can be derived from yield numbers, cost numbers and salesprice.

The profit model described above is applicable to a production linemodel that does not utilize the cell and module repair stages 214 and216. However, it should be appreciated that the profit model describedabove can be adapted for a production line model that does utilize theoptional cell and model repair stages 214 and 216, while still fallingwithin the scope of the present invention. Further, if the optional celland module repair stages 214 and 216 are used, but the cell and modulerepair rates are so low as to not make a significant contribution to theyield rates, then the above-described profit model may be applied.

III. Identifying Defects During TFT-Array Panel Testing

Each TFT-array panel is tested in the array test stage 202 using arraytesting equipment known in the art. When each TFT-array panel is testedby the array testing equipment, the TFT-array panel is driven byelectrical signals and the storage capacitor of each pixel goes throughelectrical charging and discharging operations in order to achievecertain target voltage signals. The sensor of the array test equipmentmeasures the pixel voltage on the storage capacitor of every pixel ofthe TFT-array panel. If a pixel has a defect, then the pixel voltage ofthe defected pixel is different from the pixel voltage of the normalpixels. The difference between the defected pixel voltage and the normalpixel voltage is called a “defect signal.”

FIG. 3 is a plot showing the pixel voltage distribution when half of thepixels of the TFT-array panel have positive pixel voltages and the otherhalf have negative pixel voltages. These distributions can berepresented by a statistical distribution function because of the largenumber of pixels in each TFT-array panel, and because of the sensor'sstatistical behavior. The distribution function for normal positivepixel voltages 310 is well represented by a normal distribution functionas follows:

p=N _(P) exp[−(v−V _(P))²/(2σ_(P) ²)]/√{square root over (2πσ_(P)²)},  (43)where

p represents the distribution function for normal positive pixelvoltages, N_(P) is the total number of pixels having normal positivepixel voltages, v is a pixel voltage variable, V_(P) is a mean value andσ_(P) is a standard deviation of the normal distribution function forpositive pixel voltages.

N_(P) can be obtained by subtracting the number of defective pixelshaving positive pixel voltages from the total number of pixels havingpositive pixel voltages, and can be approximated to be the total numberof pixels having positive pixel voltages because the number of defectivepixels having positive pixel voltages is far lower than the number ofnormal pixels having positive pixel voltages.

The distribution function for normal negative pixel voltages 320 issimilarly well represented by a normal distribution function as follows:

n=N _(N) exp[−(v−V _(N))²/(2σ_(N) ²)]/√{square root over (2πσ_(N)²)},  (44)where

n represents the distribution function for normal negative pixelvoltages, N_(N) is a total number of pixels having normal negative pixelvoltage, and V_(N) is a mean value and σ_(N) is a standard deviation ofnormal distribution function for negative pixel voltages.

N_(N) can be obtained by subtracting the number of defective pixelshaving negative pixel voltages from the total number of pixels havingnegative pixel voltages, and can be approximated to be the total numberof pixels having negative pixel voltages because the number of defectivepixels having negative pixel voltages is far lower than the number ofnormal pixels having negative pixel voltages. The values of V_(P),σ_(P), V_(N), and σ_(N) can be typically obtained from the array testingequipment.

The plot of FIG. 3 also shows the defective pixel voltage distributions330 (θph), 340 (θpl), 350 (θnh), and 360 (θnl). θph and θpl representthe defective pixel voltage distributions in response to driving signalsthat produce positive polarity pixel voltages. θnh and θnl representdefective pixel voltage distributions in response to driving signalsthat produce negative polarity pixel voltages.

The array testing equipment uses thresholding parameters of Vthi+,Vtlo+, Vthi−, and Vtlo− to detect the defective pixels. Pixels driven tohave positive pixel voltages are reported as defective when their pixelvoltages fall outside of the positive threshold region between Vthi+ andVtlo+. Pixels driven to have negative pixel voltages are reported asdefective when their pixel voltages fall outside of the negativethreshold region between Vthi− and Vtlo−.

Under-Killed and Over-Killed Defects

If a normal pixel exhibits a pixel voltage that is outside of thethreshold region, then the normal pixel is wrongly classified as adefective pixel. This erroneous classification is called an “over-killeddefect.” If a defective pixel exhibits a pixel voltage that is inside ofthe threshold region, then the defective pixel is wrongly characterizedas a normal pixel. This erroneous classification is called an“under-killed defect.”

Under-killed defects lower the yields at the cell inspection stage 208(Y_(C)) and/or the yields at the module inspection stage 212 (Y_(M)).Over-killed defects lower the productivity of the array repair equipmentused in the array repair stage 204. Therefore it is very important toset the right values for the thresholding parameters, in order tomaximize profit or minimize the loss of product fabrication.

IV. Effects of Bad Cells/Modules on the Number of Under-killed Defects

FIG. 4 is a block diagram showing the layout of a typical glasssubstrate 400 used in TFT-LCD manufacturing. The glass substrate 400generally consists of multiple TFT-array panels 400 a-400 i, and eachpanel is used for a display unit assembly. If the display is classifiedas a bad unit when it has just a single defect, then the number of baddisplays is determined as described below.

When there is only one defect in the glass substrate 400, the one defectcan fall on any one of the n panels. Thus, one defect causes one baddisplay unit. Accordingly, the total number of bad panels in the case ofsingle defect in the glass substrate 400 (N_(BAD-PANEL1)) is:N_(BAD-PANEL1)=1.  (45)

When there is second defect in the glass substrate 400, the seconddefect can fall on any one of the n panels. If the second defect fallson the same panel that the first defect falls on, then the second defectdoes not result in a new bad panel. However, the second defect willcause a new bad panel if it falls on one of the other panels. Thus theprobability of causing another bad panel by a second defect (P₂)becomes:P ₂=(n−1)/n.  (46)

Thus, from Equations (45) and (46), the total number of bad panels inthe case of two defects in the glass substrate (N_(BAD-PANEL2)) is:N _(BAD-PANEL2) =N _(BAD-PANEL1) +P ₂=1+(n−1)/n.  (47)

When there is third defect in the glass substrate 400, the third defectcan fall on any one of the n panels. If the third defect falls on apanel that already has any number of defects, then the third defect doesnot result in a new bad panel. However, the third defect will cause anew bad panel if it falls on a panel that has no defect. Thus, theprobability of causing another bad panel by the third defect (P₃) is:P ₃ =P _(DOUBLE)(n−1)/n+(1−P _(DOUBLE))(n−2)/n,  (48)where P_(DOUBLE) is the probability of having two defects in the samepanel, and is given by:P _(DOUBLE) =n(1/n)(1/n)=1/n.  (49)Thus, P₃ becomes:P ₃=(1/n)(n−1)/n+(1−1/n)(n−2)/n=(n−1)² /n ².  (50)

Thus, from Eqs. (47) and (50), the total number of bad panels in thecase of three defects present in the glass substrate 400(N_(BAD-PANEL3)) is:N _(BAD-PANEL3) =N _(BAD-PANEL2) +P ₃=1+(n−1)/n+(n−1)² /n ².  (51)

When there is fourth defect in the glass substrate 400, the fourthdefect can fall on any one of the n panels. If the fourth defect fallson a panel that already has any number of defects, then the fourthdefect does not result in a new bad panel. However, the fourth defectresults in a new bad panel if it falls on a panel that has no defect.Thus, the probability of causing another bad panel by the fourth defect(P₄) is:P ₄ =P _(TRIPLE)(n−1)/n+P _(DOUBLE-SINGLE)(n−2)/n+(1−P _(TRIPLE) −P_(DOUBLE-SINGLE))(n−3)/n,  (52)where P_(TRIPLE) is the probability of having three defects in the samepanel, and is given by:P _(TRIPLE) =n(1/n)(1/n)(1/n)=1/n ²,  (53)and P_(DOUBLE-SINGLE) is the probability of having two defects in thesame panel and one defect in different pane, and is given by:P _(DOUBLE-SINGLE) =n(1/n)(1/n)(n−1)/n=(n−1)/n ².  (54)Thus, P₄ becomes: P ₄=(1/n ²)(n−1)/n+((n−1)/n ²)(n−2)/n+(1−1/n ²−(n−1)/n ²)(n−3)/n=(n−1)/n ³+(n−1)(n−2)/n ³+(1−1/n ²−(n−1)/n ²)(n−3)/n=(n−1+(n−1)(n−2)+(n ²−1−(n−1))(n−3))/n ³=(n−1+(n−1)(n−2)+n(n−1)(n−3))/n³=(n−1)(1+n−2+n(n−3))/n ³=(n−1)(n ²−2n−1)/n³.  (55)

Thus, from Equations (51) and (55), the total number of bad panels inthe case of four defects present in the glass substrate 400(N_(BAD-PANEL4)) is:N _(BAD-PANEL4) =N _(BAD-PANEL3) +P ₄=1+(n−1)/n+(n−1)² /n ²+(n−1)(n²−2n−1)/n ³.  (56)

In a normal production line, it is very rare that the number of defectsper glass substrate exceeds four. If the under-killed defects of theTFT-array test equipment are the dominant cause of bad panels at celland module inspections, one can assume that the number of cell andmodule defects is proportional to the number of under-killed defects asfollows:N_(CELL-DEFECT)=αU; and  (57)N_(MODULE-DEFECT)=βU,  (58)where α and β are the proportionality constants for cell and moduledefects, respectively. Then, from Equations (45), (47), (51), (56),(57), and (58), one can obtain:N_(BAD-CELL1)=α;  (59)N _(BAD-CELL2)=α(1+(n−1)/n);  (60)N _(BAD-CELL3)=α(1+(n−1)/n+(n−1)² /n ²);  (61)N _(BAD-CELL4)=α(1+(n−1)/n+(n−1)² /n ²+(n−1)(n ²−2n−1)/n ³);  (62) N_(BAD-MODULE1)=β;  (63).N _(BAD-MODULE2)=β(1+(n−1)/n);  (64)N _(BAD-MODULE3)=β(1+(n−1)/n+(n−1)² /n ²); and  (65)N _(BAD-MODULE4)=β(1+(n−1)/n+(n−1)² /n ²+(n−1)(n ²−2n−1)/n ³),  (66)where N_(BAD-CELL) and N_(BAD-MODULE) are the number of bad cells andmodules, respectively.

If the number of under-kill defects per glass substrate does not exceedapproximately four, and the number of panels per glass substrate (n) issignificantly larger than 1, then one obtains:N_(BAD-CELL1)=α;  (67)N_(BAD-CELL2)≅2α;  (68)N_(BAD-CELL3)≅3α;  (69)N_(BAD-CELL4)≅4α;  (70)N_(BAD-MODULE1)=β;  (71)N_(BAD-MODULE2)≅2β;  (72)N_(BAD-MODULE3)≅3β; and  (73)N_(BAD-MODULE4)≅4β.  (74)

Equations (67) to (70) can be summarized as:N_(BAD-CELL)≅Uα,  (75)and Equations (71) to (74) can be summarized as: N_(BAD-MODULE)≅Uβ.  (76)V. Test Recipes

Ideally, the array testing equipment is supposed to identify all thedefective pixels in the TFT-array panel without misclassifying normalpixels as a defective pixels. However, in reality, the array testingequipment may miss actual defective pixels (under-killed defects) andwrongly classify normal pixels as defective pixels (over-killeddefects).

The phrase “test recipe” is used herein to refer to the testingparameters used by the array testing equipment, e.g., the amplitude,timing and shape of the pixel driving signal, and the thresholdingparameters used to classify pixels as normal or defective. A currentlyused recipe is referred to herein as a “primary test recipe”, and itsresult is called a “primary test result”. A proposed new test recipe isreferred to herein as a “new test recipe”, and its result is called a“new test result.”

A new test recipe is classified herein as either a “new thresholdingtest recipe” or a “new distribution function test recipe.” A newthresholding recipe is one that only changes the thresholdingparameters, without affecting the voltage distribution functions of thenormal and defective pixels. A new distribution function recipe is onethat changes the voltage distribution functions of the normal and/ordefective pixels.

VI. Effects of Under-Killed Defects on Profits

When a new test recipe is used in the array testing equipment, thenumbers of under-killed and over-killed defects may change from those ofthe primary test recipe. A method for determining the effects thatunder-killed defects have on the yields and profits in TFT-LCDmanufacturing will now be described. The method described below assumesthat the optional cell repair and module repair stages 214 and 216 arenot implemented.

If under-killed defects are the dominant cause of bad panels at the cellinspection stage 208 (O_(CB) in FIG. 2), then one can assume that therate of bad panels at the cell inspection stage 208 is proportional tothe number of under-killed defects (refer to Equation (75)), and obtainthe following expression:O _(CB) /I _(C) :U=O′ _(CB) /I′ _(C) :U′,  (77)where U is the number of under-killed defects for the primary testrecipe and U′ is the number of under-killed defects for the new testrecipe. Then, one obtains:O′ _(CB) /I′ _(C) =O _(CB) U′/(I _(C) U).  (78)Without the optional cell and module repair stages 214 and 216,O _(CB) =I _(C) −O _(CG).  (79)Thus, with Equation (78), one obtains:(I′ _(C) −O′ _(CG))/I′ _(C)=(I _(C) −O _(CG))U′/(I _(C) U),  (80)which becomes:1−O′ _(CG) /I′ _(C)=(1−O _(CG) /I _(C))U′/U.  (81)

From Equations (11) and (81), one obtains:Y′ _(C)=1−(1−Y _(C))U′/U.  (82)Then, the improvement of the yield at the cell inspection stage 208(E_(YC)) can be expressed as:E _(YC) ≡Y′ _(C) −Y _(C)=(1−Y _(C))(1−U′/U).  (83)

If the under-killed defects are the dominant cause of the bad panels atthe module inspection stage 212 (O_(MB) in FIG. 2), then one can alsoassume that the rate of bad panels at the module inspection stage 212 isproportional to the number of under-killed defects (refer to Equation(76)), and obtain following expression:O _(MB) /I _(M) :U=O′ _(MB) /I′ _(M) :U′.  (84)

Then, one obtains:O′ _(MB) /I′ _(M) =O _(MB) U′/(I _(M) U).  (85)Since O_(MB)=I_(M)−O_(MG) without the optional cell and module repairstages 214 and 216, with Equation (85), one obtains:(I′ _(M) −O′ _(MG))/I′ _(M)=(I _(M) −O _(MG))U′/(I _(M) U),  (86)which becomes:1−O′ _(MG) /I′ _(M)=(1−O _(MG) /I _(M))U′/U.  (87)

From Equations (12) and (87), one obtains:Y′ _(M)=1−(1−Y _(M))U′/U.  (88)Then, the yield improvement at the module inspection stage 212 (E_(YM))can be expressed as:E _(YM) ≡Y′ _(M) −Y _(M)=(1−Y _(M))(1−U′/U).  (89)

From Equations (82), (88), and (26), one obtains:

 P≅(I _(AR) −I′ _(AR))C _(R)+(Y _(C)−(1−(1−Y _(C))U′/U))I _(C)(C _(M) +C_(MI))+((1−(1−Y _(M))U′/U)(1−(1−Y _(C))U′/U)−Y _(M) Y _(C))P _(VALUE) I_(C)  (90)

The effect of a new test recipe on the over-killed panels, Δ

, and on the under-killed panels, ΔU, can be expressed as:Δ

=

−

′=γ(

−

′)=γΔ

; and  (91)ΔU=U−U′=γ(U−U′)=γΔU,  (92)where

and

′ are the numbers of over-killed defects for the primary and new testrecipes, respectively, U and U′ are the numbers of under-killed defectsfor the primary and new test recipes, respectively, and γ is aproportionality constant relating the number of defects to the number ofbad panels, as shown by Equations (45), (47), (51), and (56).

Then, one can obtain, with the assumption O_(ATB)≅O′_(ATB),I _(AR) −I′ _(AR)=(R+−U−O _(ATB))−(R+′−U′−O′ _(ATB))≅(

−

′)−(U−U′),  (93)where R is the number of bad panels with real defects.

From Equations (91), (92), and (93), one obtains:I _(AR) −I′ _(AR) ≅Δ−ΔU=γ(Δ

−ΔU).  (94)Using Equation (94) in Equation (90), one obtains:P≅γ(Δ

−ΔU)C _(R)+(Y _(C)−(1−(1−Y _(C))U′/U))I _(C)(C _(M) +C _(MI))+((1−(1−Y_(M))U′/U)(1−(1−Y _(C))U′/U)−Y _(M) Y _(C))P _(VALUE) I _(C).  (95)

-   -   VI. Profit Maximization by Threshold Optimization

The effect of a new thresholding test recipe on yields at the cellinspection stage 208 and the module inspection stage 212, and on theproductivity of the array repair equipment will now be described. Itwill also be shown how profit can be maximized by optimizingthresholding parameters.

As discussed above, in order to have a reference for optimization of thethresholding parameters, the current test recipe of the array testequipment is called the primary test recipe, and its test result iscalled the primary test result. The current thresholding parameters ofVthi+, Vtlo+, Vthi−, and Vtlo− are called primary thresholdingparameters. If one wants to evaluate the effect of new thresholdingparameters on a production batch that has been already been processedthrough final module inspection using the primary test recipe, then onecan use the evaluation method that will now be described.

If the defective pixel voltage distribution is already known, then thenumber of under-killed defects for the primary test recipe can beobtained by:U=Unl+Unh+Upl+Uph,  (96)where:Unl=∫ _(Vtlo−) ^(Vdc−) θnl dv, Unh=∫ _(Vdb−) ^(Vthi−) θnh dv, Upl=∫_(Vtlo+) ^(Vdb+) θpl dv, Uph=∫ _(Vdc+) ^(Vthi+) θph dv.

If the normal pixel voltage distribution is already known, then thenumber of over-killed defects for the primary test recipe can beobtained by:

=

nl+nh+pl+ph,  (97)where:

nl=∫ _(−∞) ^(Vtlo−) n dv, nh=∫ _(Vthi−) ⁰ n dv, pl=∫ ₀ ^(Vtlo+) p dv,ph=∫ _(Vthi+) ^(∞) p dv.

The Vtlo− thresholding value is scanned using variable vtlo−, whilekeeping the other threshold voltages at the fixed primary values. Inthis way, the number of under-killed and over-killed defects for the newthresholding recipe can be obtained by:U′=U′nl+Unh+Upl+Uph; and  (98)

′=

′nl+nh+pl+ph,  (99)where:U′nl=∫ _(vtlo−) ^(Vdc−) θnl dv and

′nl=∫ _(−∞) ^(vtlo−) n dv.

From Equations (91), (92), and (96)-(99), one obtains:Δ

=

−

′=

nl−′nl; and  (100)ΔU=U−U′=Unl−U′nl.  (101)

From Equations (82), (83), (88), (89), (96), and (98), one obtains:Y′ _(C)=1−(1−Y _(C))(U′nl+Unh+Upl+Uph)/(Unl+Unh+Upl+Uph);  (102)E _(YC) ≡Y′ _(C) −Y _(C)=(1−Y_(C))(1−(U′nl+Unh+Upl+Uph)/(Unl+Unh+Upl+Uph);  (103)Y′ _(M)=1−(1−Y _(M))(U′nl+Unh+Upl+Uph)/(Unl+Unh+Upl+Uph); and  (104)E _(YM) ≡Y′ _(M) −Y _(M)=(1−Y_(M))(1−(U′nl+Unh+Upl+Uph)/(Unl+Unh+Upl+Uph)).  (105)

From Equations (95), (96), (98), (100), and (101), one obtains:P≅γ(

nl−′nl−Unl+U′nl)C _(R)+(Y _(C)−(1−(1−Y_(C))(U′nl+Unh+Upl+Uph)/(Unl+Unh+Upl+Uph)))I _(C)(C _(M) +C _(MI))+((1−(1−Y_(M))(U′nl+Unh+Upl+Uph)/(Unl+Unh+Upl+Uph))(1−(1−Y_(C))(U′nl+Unh+Upl+Uph)/(Unl+Unh+Upl+Uph))−Y _(M) Y _(C))P _(VALUE) I_(C)  ((106)

Therefore, profit maximization can be achieved by taking the maximumvalue of P while the variable vtlo− is scanned around the primarythresholding parameter of Vtlo−.

The Vthi− thresholding value can also be scanned using variable vthi−,while keeping the other thresholding voltages at the fixed primaryvalues. The number of under-killed and over-killed defects for the newthresholding recipe can then be obtained by:U′=Unl+U′nh+Upl+Uph; and  (107)

′=

nl+′nh+pl+ph,  (108)where:U′nh=∫ _(Vdb−) ^(vthi−) θnh dv and

′nh=∫ _(vthi−) ⁰ n dv.

From Equations (91), (92), (96), (97), (107), and (108), one obtains:Δ

=

−

′=

nh−′nh; and  (109)ΔU=U−U′=Unh−U′nh.  (110)

From Equations (82), (83), (88), (89), (96), and (107), one obtains:Y′ _(C)=1−(1−Y _(C))(Unl+U′nh+Upl+Uph)/(Unl+Unh+Upl+Uph);  (111)E _(YC) ≡Y′ _(C) −Y _(C)=(1−Y_(C))(1−(Unl+U′nh+Upl+Uph)/(Unl+Unh+Upl+Uph));  (112)Y′ _(M)=1−(1−Y _(M))(Unl+U′nh+Upl+Uph)/(Unl+Unh+Upl+Uph); and  (113) E _(YM) ≡Y′ _(M) −Y _(M)=(1−Y_(M))(1−(Unl+U′nh+Upl+Uph)/(Unl+Unh+Upl+Uph)).  (114)

From Equations (95), (96), (107), (109), and (110), one obtains:P≅γ(

nh−′nh−Unh+U′nh)C _(R)+(Y _(C)−(1−(1−Y_(C))(Unl+U′nh+Upl+Uph)/(Unl+Unh+Upl+Uph)))I _(C)(C _(M) +C _(MI))+((1−(1−Y_(M))(Unl+U′nh+Upl+Uph)/(Unl+Unh+Upl+Uph))(1−(1−Y_(C))(Unl+U′nh+Upl+Uph)/(Unl+Unh+Upl+Uph))−Y _(M) Y _(C))P _(VALUE) I_(C)  (115)Therefore, profit maximization can be achieved by taking the maximumvalue of P, while the variable vthi− is scanned around the primaryparameter of Vthi−.

Thresholding value Vdo+ can also be scanned using variable vtlo+, whilekeeping the other thresholding voltages at the fixed primary values. Thenumber of under-killed and over-killed defects for the new thresholdingrecipe can then be obtained by:U′=Unl+Unh+U′pl+Uph; and  (116)

′=

nl+nh+′pl+ph,  (117)where:U′pl=∫ _(vtlo+) ^(Vdb+) θpl dv and

′pl=∫ ₀ ^(vtlo+) p dv.

From Equations (91), (92), (96), (97), (116), and (117), one obtains:Δ

=

−

′=

pl−′pl; and  (118)ΔU=U−U′=Upl−U′pl.  (119)

From Equations (82), (83), (88), (89), (96), and (116), one obtains:Y′ _(C)=1−(1−Y_(C))(Unl+Unh+U′pl+Uph)/(Unl+Unh+Upl+Uph);  (120) E _(YC) ≡Y′ _(C) −Y _(C)=(1−Y_(C))(1−(Unl+Unh+U′pl+Uph)/(Unl+Unh+Upl+Uph));  (121)Y′ _(M)=1−(1−Y _(M))(Unl+Unh+U′pl+Uph)/(Unl+Unh+Upl+Uph); and  (122)E _(YM) ≡Y′ _(M) −Y _(M)=(1−Y_(M))(1−(Unl+Unh+U′pl+Uph)/(Unl+Unh+Upl+Uph))  (123)

From Equations (95), (96), (116), (118), and (119), one obtains:P≅γ(

pl−′pl−Upl+U′pl)C _(R)+(Y _(C)−(1−(1−Y_(C))(Unl+Unh+U′pl+Uph)/(Unl+Unh+Upl+Uph)))I _(C)(C _(M) +C _(MI))+((1−(1−Y_(M))(Unl+Unh+U′pl+Uph)/(Unl+Unh+Upl+Uph))(1−(1−Y_(C))(Unl+Unh+U′pl+Uph)/(Unl+Unh+Upl+Uph))−Y _(M) Y _(C))P _(VALUE) I_(C).  (124)Therefore, profit maximization can be achieved by taking the maximumvalue of P, while the variable vtlo+ is scanned around the primaryparameter of Vtlo+.

Thresholding value Vthi+ can also be scanned using variable vthi+, whilekeeping the other thresholding voltages at the fixed primary values. Thenumber of under-killed and over-killed defects for the new thresholdingrecipe can then be obtained by:U′=Unl+Unh+Upl+U′ph; and  (125)

′=

nl+nh+pl+′ph,  (126)where:U′ph=∫ _(Vdc+) ^(vthi+) θph dv and O′ph=∫ _(vthi+) ^(∞) p dv.

From Equations (91), (92), (96), (97), (125), and (126), one obtains:Δ

=

−

′=

ph−′ph; and  (127)ΔU=U−U′=Uph−U′ph.  (128)

From Equations (82), (83), (88), (89), (96), and (125), one obtains:

 Y′ _(C)=1−(1−Y _(C))(Unl+Unh+Upl+U′ph)/(Unl+Unh+Upl+Uph);  (129)E _(YC) ≡Y′ _(C) −Y _(C)=(1−Y_(C))(1−(Unl+Unh+Upl+U′ph)/(Unl+Unh+Upl+Uph));  (130)Y′ _(M)=1−(1−Y _(M))(Unl+Unh+Upl+U′ph)/(Unl+Unh+Upl+Uph); and  (131)E _(YM) ≡Y′ _(M) −Y _(M)=(1−Y_(M))(1−(Unl+Unh+Upl+U′ph)/(Unl+Unh+Upl+Uph)).  (132)

From Equations (95), (96), (125), (127), and (128), one obtains:P≅γ(

ph−′ph−Uph+U′ph)C _(R)+(Y _(C)−(1−(1−Y_(C))(Unl+Unh+Upl+U′ph)/(Unl+Unh+Upl+Uph)))I _(C)(C _(M) +C _(MI))+((1−(1−Y_(M))(Unl+Unh+Upl+U′ph)/(Unl+Unh+Upl+Uph))(1−(1−Y_(C))(Unl+Unh+Upl+U′ph)/(Unl+Unh+Upl+Uph))−Y _(M) Y _(C))P _(VALUE) I_(C).  (133)Therefore, profit maximization can be achieved by taking the maximumvalue of P, while the variable vthi+ is scanned around the primaryparameter of Vthi+.

Thus, it has been shown how new values for the thresholding parametersof Vtlo−, Vthi−, Vtlo+, and Vthi+ can be determined that give themaximum profit when the defective and normal pixel voltage distributionsare already known. One can use the methodology described above tooptimize the thresholding parameters based on presumed or knowndistributions of defective and normal pixel voltages.

FIG. 5 is a flow chart of a method of generating the distributionfunctions for normal pixels and defective pixels in an actual productionenvironment. All the equations having integral expressions should besolved in such a way that the integration is performed numerically bycounting the number of either good pixels for

n and

p, or the number of defective pixels for θnl, θnh, θpl and θph, as thethresholding parameter is scanned.

The method starts at step 500, and proceeds to step 505, where a newthresholding parameter set is used that will classify more pixels asdefects than those classified by the primary thresholding parameters.The resulting defect file is labeled “proto defect file”.

Then, at step 510, the proto defect file is reprocessed using theprimary thresholding parameters, in order to convert the proto defectfile to a primary defect file. The primary defect file is then comparedto the proto defect file, and the additional defective pixels reportedin the proto defect file are labeled “additional defects”.

Next, at step 515, the defective panels are repaired based oninformation in the primary defect file. The process proceeds to step520, where the cells are assembled and inspected.

Then, at step 525, the modules are assembled and inspected. Next, atstep 530, if the “additional defects” are detected as real defectivepixels during the cell or module inspections, the “additional defects”are used to construct θnl, θnh, θpl, and θph in accordance with thepolarity and magnitude of the pixel voltages, as shown in FIG. 3. Theprocess then ends at step 535.

The analysis described above is applicable to a production line modelthat does not utilize the optional cell and module repair stages 214 and216. However, it should be appreciated that the analysis described abovecan be adapted for a production line model that does utilize theoptional cell and model repair stages 214 and 216, while still fallingwithin the scope of the present invention. Further, if the optional celland module repair stages 214 and 216 are used, but the cell and modulerepair rates are so low as to not make a significant contribution to theyield rates, then the above-described analysis may be applied.

VII. Profit Evaluation Using New Distribution Function Test Recipe

It was described above how profit can be maximized by optimizing thethresholding parameters, based on the assumption that the under-killeddefects are the dominant cause of bad panels at the cell and moduleinspection stages 208 and 212. In order to further improve the profit, anew distribution function test recipe can also be applied to theTFT-array test equipment.

In order to verify the effect of the new distribution function testrecipe, one may split a very large production run into two groups, andtest one group using the primary test recipe and the second group usingthe new distribution function test recipe. Then, the yields at the celland module inspection stages 208 and 212 for each group can be compared.However, this method would take a long time due to the very large samplequantity required to minimize process fluctuations, and also takes thehigh risk of sacrificing many sample units if one uses an improper newdistribution function test recipe.

Thus, it is preferable to evaluate the new distribution function testrecipe using the same production run that was already tested with theprimary test recipe, in order to obtain a fair comparison between theprimary and new distribution function test recipes, without the need forlarge numbers of panels. The new distribution function test recipegenerates different distribution functions for normal and defectivepixel voltages from those generated by the primary test recipe, even forthe same sample production run. The effects of the new distributionfunction test recipe on the yield and profit are then evaluated.

First, at the array test stage 202, the sample production run is testedwith the primary test recipe, and the test results is labeled “primarydefect file” (DF_(PRIME)). Then, the same sample production run isretested with the new distribution function test recipe, and that testresult is called “new defect file” (DF_(NEW)).

The sample production run then proceeds to the array repair stage 204,and only the pixels commonly reported as defective in DF_(PRIME) andDF_(NEW) are reviewed by the operator of the TFT-array repair equipment.The operator then attempts to repair the pixels when the defects arevisually confirmed. The sample production run then proceeds to nextstages, which is assumed to not include the optional cell and modulerepair stages 214 and 216.

For evaluation of the new distribution function test recipe, one needsto sort out the defects reported in DF_(PRIME) and DF_(NEW) based on therepair actions performed on the defects, and the results of cell andmodule inspections at the cell and module inspection stages 208 and 212.

The table shown in FIG. 6 and the flow chart shown in FIG. 7 illustratehow the results of the array test stage 202, array repair stage 204,cell inspection stage 208 and module inspection stage 212 are used tosort out the defective pixels discovered.

The process of FIG. 7 starts at step 700, and proceeds to steps 705,where the DF_(PRIME) and DF_(NEW) are obtained from the table of FIG. 6and sorted as follows:

-   Common defects, CD=(GGc+GGm+OOn+GGcr+GGmr+GGr);-   DF_(PRIME) unique defects, DPu=(GUc+GUm+OGn); and-   DF_(NEW) unique defects, DNu=(UGc+UGm+GOn).

The process then continues to step 710 where, using the input to thearray repair stage 204, CD is sorted into:

-   CD1=(GGc+GGm+OOn); and-   CD2=(GGcr+GGmr+GGr).    The array repair stage looks at only CD and parts of them are sorted    as CD2 when a repair action is taken.

Next, at step 715, using the input to the cell inspection stage 208, thefollowing sorting is done:

-   CD1 into GGc and CD1 a=(GGm+OOn);-   CD2 into GGcr and CD2 a=(GGmr+GGr);-   DPu into GUc and DPu1=(GUm+OGn);-   DNu into UGc and DNu1=(UGm+GOn); and    new cell defects as UUc.

Then, at step 720, using the input to the module inspection stage, thefollowing sorting is done:

-   CD1 a into GGm and OOn;-   CD2 a into GGmr and GGr;-   DPu1 into GUm and OGn;-   DNu1 into UGm and GOn; and    new cell defect as UUm.

The process then ends at step 725. From FIG. 6, the total cell defectfor the sample production (T_(CDc)) can be obtained as:T _(CDc) =GGc+GUc+GGcr+UGc+UUc.  (134)

The effect of a new distribution function test recipe on the cell yieldwill now be considered. Total cell defect, if only the primary testrecipe had been applied, is shown in the table of FIG. 8, and is givenby:T _(CD) =T _(CDc) −Nc GUc,  (135)because all GUc pixels should have been identified as defects and Ncportion of them could have been repaired to good pixels and would haveincreased GGr. GGr can be defined as:GGr=GGrc+GGrm,  (136)where GGrc is the number of good repaired pixels, which would have beendetected as defects at the cell inspection stage 208 had they not beenrepaired, and GGrm is the number of good repaired pixels which wouldhave been detected as defects at the module inspection stage 212 hadthey nor been repaired. One can then assume that the number ofsuccessfully repaired pixels (Nc) would have followed the successfulrepair rate for the commonly detected defects, and obtain an expressionfor Nc as follows:Nc=GGrc/(GGcr+GGrc).  (137)

One can assume that the successful repair rate of cell defects is thesame as that of module defects (GGcr:GGmr=GGrc:GGrm) and obtain:GGrc=GGcr GGrm/GGmr.  (138)

From Equations (136) and (138), one obtains:GGrc=GGcr(GGr−GGrc)/GGmr;  (139)GGmr GGrc+GGcr GGrc=GGcr GGr; and  (140)GGrc=GGcr GGr/(GGmr+GGcr).  (141)

From Equations (134), (135), (137) and (141), one obtains:Nc=(GGcrGGr/(GGmr+GGcr))/(GGcr+(GGcrGGr/(GGmr+GGcr)))=GGcrGGr/(GGcr(GGmr+GGcr)+GGcrGGr)=GGr/(GGmr+GGcr+GGr); and  (142)T _(CD) =T _(CDc) −Nc GUc=GGc+(1−Nc)GUc+GGcr+UGc+UUc.  (143)

From Equations (142) and (143), one obtains:T _(CD) =GGc+(GGmr+GGcr)GUc/(GGmr+GGcr+GGr)+GGcr+UGc+UUc.  (144)

Total cell defects, if only the new distribution function test recipehad been applied, is shown in the table of FIG. 9, and is given by:T′ _(CD) =T _(CDc) −Nc UGc,  (145)because all the UGc pixels should have been identified as defects and Ncnumber of them could have been repaired to good pixels and would haveincreased GGr.

From Equations (134) and (145), one obtains:T′ _(CD) =T _(CDc) −Nc UGc=GGc+GUc+GGcr+(1−Nc)UGc+UUc.  (146)

From Equations (142) and (146), one obtains:T′ _(CD) =GGc+GUc+GGcr+(GGmr+GGcr)UGc/(GGmr+GGcr+GGr)+UUc.  (147)

From Equations (143) and (146), the effect on total cell defects(ε_(TCD)) due to using the new distribution function test recipe onlyinstead of only the primary test recipe is given by:ε_(TCD) =T _(CD) −T′ _(CD) =Nc UGc−Nc GUc=Nc(UGc−GUc).  (148)

From FIG. 6, the total module defects for the sample production(T_(MDc)) can be obtained as:T _(MDc) =GGm+GUm+GGmr+UGm+UUm.  (149)

The effect of the new distribution function test recipe on the moduleyield will now be considered. Total module defects, if only the primarytest recipe had been applied is shown in FIG. 8, and is given by:

 T _(MD) =T _(MDc) −Nm GUm,  (150)

because all GUm pixels should have been identified as defects, and Nmnumber of them could have been repaired to good pixels, which would haveincreased GGr. Then, one can assume that the portion of successfullyrepaired pixels follows the successful repair rate for the commonlydetected defects, and obtain the following expression for Nm:Nm=GGrm/(GGmr+GGrm).  (151)

From Equation (138), one obtains:GGrm=GGmr GGrc/GGcr.  (152)

From Equations (136) and (152), one obtains:GGrm=GGmr(GGr−GGrm)/GGcr;  (153)GGrm GGcr+GGmr GGrm=GGmr GGr; and  (154)GGrm=GGmr GGr/(GGcr+GGmr).  (155)

From Equations (149), (150), (151) and (155), one obtains:Nm=(GGmrGGr/(GGcr+GGmr))/(GGmr+(GGmrGGr/(GGcr+GGmr)))=GGmrGGr/(GGmr(GGcr+GGmr)+GGmrGGr)=GGr/(GGcr+GGmr+GGr); and  (156)T _(MD) =T _(MDc) −NmGUm=GGm+(1−Nm)GUm+GGmr+UGm+UUm.  (157)

From Equations (156) and (157), one obtains:T _(MD) =GGm+(GGcr+GGmr)GUm/(GGcr+GGmr+GGr)+GGmr+UGm+UUm.  (158)

Total module defects, if only the new distribution function test recipehad been applied, is shown in FIG. 9, and is given by:

 T′ _(MD) =T _(MDc) −Nm UGm,  (159)

because all UGm pixels should have been identified as defects, and Nmnumber of them could have been repaired to good pixels and would haveincreased GGr.

From Equations (149) and (159), one obtains:T′ _(MD) =T _(MDc) −NmUGm=GGm+GUm+GGmr+(1−Nm)UGm+UUm.  (160)

From Equations (156) and (160), one obtains:T′ _(MD) =GGm+GUm+GGmr+(GGcr+GGmr)UGm/(GGcr+GGmr+GGr)+UUm.  (161)

From Equations (157) and (160), the effect on total module defects(ε_(TMD)) due to using the new distribution function test recipe onlyinstead of only the primary test recipe is given by:ε_(TMD) =T _(MD) −T′ _(MD) =Nm UGm−Nm GUm=Nm(UGm−GUm).  (162)

The effect of the new distribution function test recipe on over-killwill now be considered. From Equation (91) and FIG. 6, one can obtain:Number of over-killed panels of primary-test-only,

=γ

=γ(OOn+OGn);  (163)Number of over-killed panels of new-test-only,

′=γ

′=γ(OOn+GOn); and  (164)Δ

=

−

′=γ(OGn−GOn).  (165)

In TFT-LCD manufacturing, because of the possibility of unsuccessfulrepair work, the under-killed defects may not be the only dominatingsource for bad panels at cell or module inspections. Thus, fromEquations (45), (47), (51) and (56), one can assume that the rate of badpanels at the cell inspection stage 208 is proportional to the number oftotal cell defects, and obtain following expressions:O _(CB) /I _(C) :T _(CD) =O′ _(CB) /I′ _(C) :T′ _(CD); and  (166)O′ _(CB) /I′ _(C) =O _(CB) T′ _(CD)/(I _(C) T _(CD))).  (167)

From Equations (79) and (167), one obtains:(I′ ^(C) −O′ _(CG))/I′ _(C)=(I _(C) −O _(CG))T′ _(CD)/(I _(C) T _(CD));and  (168)1−O′ _(CG) /I′ _(C)=(1−O _(CG) /I _(C))T′ _(CD))/T _(CD).  (169)

From Equations (11) and (169), one obtains:Y′ _(C)=1−(1−Y _(C))T′ _(CD) /T _(CD).  (170)Then, the improvement of cell inspection yield (E_(YC)) can be expressedas:E _(YC) ≡Y′ _(C) −Y _(C)=(1−Y _(C))(1−T′ _(CD) /T _(CD)).  (171)

One can also assume that the rate of bad panels at the module inspectionstage 212 is proportional to the number of total module defects, andobtain following expression:O _(MB) /I _(M) :T _(MD) =O′ _(MB) /I′ _(M) :T′ _(MD).  (172)Then, one obtains:O′ _(MB) /I′ _(M) =O _(MB) T′ _(MD)/(I _(M) T _(MD)).  (173)

From Equation (173), since O_(MB)=I_(M)−O_(MG) without the optional celland module repair stages 214 and 216, one obtains:(I′ _(M) −O′ _(MG))/I′ _(M)=(I _(M) −O _(MG))T′ _(MD)/(I _(M) T _(MD));and  (174) 1−O′ _(MG) /I′ _(M)=(1−O _(MG) /I _(M))T′ _(MD) /T _(MD).  (175)

From Equations (12) and (175), one obtains:Y′ _(M)=1−(1−Y _(M))T′ _(MD) /T′ _(MD).  (176)Then, the improvement in the module inspection yield (E_(YM)) can beexpressed as:E _(YM) ≡Y′ _(M) −Y _(M)=(1−Y _(M))(1−T′ _(MD) /T _(MD)).  (177)

Then, one can obtain an expression for the profit increase by usingEquations (170), (171), (176), (177), and (26), as follows:P≅(I _(AR) −I′ _(AR))C _(R)+(Y _(C)−1)(1−T′ _(CD) /T _(CD))I _(C)(C _(M)+C _(MI))+((1−(1−Y _(M))T′ _(MD) /T _(MD))(1−(1−Y _(C))T′ _(CD) /T_(CD))−Y _(M) Y _(C))P _(VALUE) I _(C).  (178)

Using Equation (94) in Equation (178), one obtains:P≅(Δ

−ΔU)C _(R)+(Y _(C)−1)(1−T′ _(CD) /T _(CD))I _(C)(C _(M) +C_(MI))+((1−(1−Y _(M))T′ _(MD) /T _(MD))(1−(1−Y _(C))T′ _(CD) /T _(CD))−Y_(M) Y _(C))P _(VALUE) I _(C).  (179)

The effect of the new distribution function test recipe on under-killwill now be considered. From Equation (92) and FIG. 6, one can obtain:Number of under-killed panels of primary-test-only,U=γU=γ(UGc+UUc+UGm+UUm); and  (180)Number of under-killed panels of new-test-only,U′=γU′=γ(GUc+GUm+UUc+UUm),  (181)where U and U′ are the numbers of under-killed defects for the primaryand new distribution function test recipes, respectively. From Equations(92), (180) and (181), one obtains the following expression for theeffect of the new distribution function test recipe on the under-killedpanels:ΔU=U−U′=γ(UGc+UGm−GUc−GUm).  (182)

Using Equations (165) and (182) in Equation (179), one obtains:P≅γ(OGn−GOn−UGc−UGm+GUc+GUm)C _(R)+(Y _(C)−1)(1−T′ _(CD) /T _(CD))I_(C)(C _(M) +C _(MI))+((1−(1−Y _(M))T′ _(MD) /T _(MD))(1−(1−Y _(C))T′_(CD) /T _(CD))−Y _(M) Y _(C))P _(VALUE) I _(C).  (183)

The values of Y_(C) and Y_(M) can be obtained from a recent productionthat was tested with the primary test recipe, under the assumption thatthe yields between the recent and sample productions are the same. Thevalues of Y_(C) and Y_(M) can also be obtained from the sampleproduction, as will now be explained.

One can obtain expressions for Y_(C) and Y_(M), similar to theexpressions for Y′_(C) and Y′_(M) shown in Equations (170) and (176),from the assumption that the rate of bad panels at cell and moduleinspection stages 208 and 212 is proportional to the number of totalcell and module defects:Y _(C)=1−(1−Y _(Cc))T _(CD) /T _(CDc); and  (184)Y _(M)=1−(1−Y _(Mc))T _(MD) /T _(MDc),  (185)where Y_(Cc) and Y_(Mc) are the cell and module yields, respectively,for the sample production in which only the pixels commonly reported asdefects in DF_(PRIME) and DF_(NEW) are sent to the TFT-array repairequipment.

From Equations (134), (144), (149), (158), (184) and (185), one obtains:

 Y _(C)=1−(1−Y_(Cc))(GGc+(GGmr+GGcr)GUc/(GGmr+GGcr+GGr)+GGcr+UGc+UUc)/(GGc+GUc+GGcr+UGc+UUc);and  (186)Y _(M)=1−(1−Y_(Mc))(GGm+(GGcr+GGmr)GUm/(GGcr+GGmr+GGr)+GGmr+UGm+UUm)/(GGm+GUm+GGmr+UGm+UUm).  (187)

The values of I_(C), I_(AR), and I_(M) can be obtained from the recentproduction with the same quantity of I_(A) that was tested with theprimary test recipe, under the assumption that the yields are the samebetween the recent and sample productions. The values of I_(C), I_(AR),and I_(M) can also be obtained from the sample production, as will nowbe described.

In regular production of TFT-LCDs, one can assume thatO_(ATB)+O_(ARB)≅O_(ATBc)+O_(ARBc) (c denotes the sample production),because the bad panels usually go to next process stage as a portion ofthe larger TFT-array base plate. If the assumptionO _(ATB) +O _(ARB) ≅O _(ATBc) +O _(ARBc)  (188)is valid, then withI _(C) =I _(A)−(O _(ATB) +O _(ARB)) and  (189)I _(Cc) =I _(A)−(O _(ATBc) +O _(ARBc)),  (190)one obtains:I_(C) ≅I _(Cc)  (191)

From Equations (93), (163), (164), (180), (181) and FIG. 6, one obtainsthe following expressions for the sample production, in which only thedefects detected both by the primary and new distribution function testrecipes are sent to the TFT-array repair equipment:I _(AR) −I _(ARc)=(R+−U−O _(ATB))−(R+c−Uc−O _(ATBc))≅(

−

c)−(U−Uc),  (192)where O_(ATB)−O_(ATBc)≅0 is assumed;Over-killed panels of sample production,

c=∩′=γOOn; and  (193)Under-killed panels of sample production,Uc=U∪U′=γ(UGc+UUc+UGm+UUm+GUc+GUm).  (194)

From Equations (163), (180), (192), (193) and (194), one obtains:I _(AR) −I_(ARc)≅γ(OOn+OGn−OOn)−γ(UGc+UUc+UGm+UUm−(UGc+UUc+UGm+UUm+GUc+GUm))=γ(OGn+GUc+GUm).  (195)

The value of γ can be obtained with the assumption that O_(ATBc) is verysmall compared with other parameters. From Equations (192), (193), (194)and FIG. 6, one obtains:I _(ARc)=R+c−Uc=γ(GGc+GUc+GGm+GUm+GGcr+GGmr+GGr+UGc+UUc+UGm+UUm+OOn−(UGc+UUc+UGm+UUm+GUc+GUm))=γ(GGc+GGm+GGcr+GGmr+GGr+OOn).  (196)Thus, from Eq. (196), one obtains:γ=I _(ARc)/(GGc+GGm+GGcr+GGmr+GGr+OOn)  (197)

From Equations (195) and (197), one obtains:I _(AR)≅γ(OGn+GUc+GUm)+I _(ARc) =I_(ARc)(OGn+GUc+GUm)/(GGc+GGm+GGcr+GGmr+GGr+OOn)+I _(ARc) =I_(ARc)(OGn+GUc+GUm+GGc+GGm+GGcr+GGmr+GGr+OOn)/(GGc+GGm+GGcr+GGmr+GGr+OOn).  (198)

From FIG. 2, without the optional cell and module repair stages 214 and216, and Equation (191), one obtains:I _(M) =O _(CG) =I _(C) −O _(CB); and  (199)I _(Mc) =O _(CGc) =I _(Cc) −O _(CBc) ≅I _(C) −O _(CBc).  (200)From Equations (199) and (200), one obtains:I _(M) ≅I _(Mc) +O _(CBc) −O _(CB).  (201)

From Equation (45), (47), (51) and (56), one can assume that the numberof bad panels at the cell inspection stage 208 is proportional to thenumber of total cell defects, and obtain the following expressions:O_(CB)=δT_(CD); and  (202)O_(CBc)=δT_(CDc),  (203)where δ is a proportionality constant.

From Equations (134) and (203), one obtains:δ=O _(CBc) /T _(CDc) =O _(CBc)/(GGc+GUc+GGcr+UGc+UUc).  (204)

From Equations (144), (202) and (204), one obtains:O _(CB)=(GGc+(GGmr+GGcr)GUc/(GGmr+GGcr+GGr)+GGcr+UGc+UUc)O_(CBc)/(GGc+GUc+GGcr+UGc+UUc).  (205)Thus, from Equations (201) and (205), one obtains:I _(M) ≅I _(Mc) +O _(CBc)−(GGc+(GGmr+GGcr)GUc/(GGmr+GGcr+GGr)+GGcr+UGc+UUc)O _(CBc)/(GGc+GUc+GGcr+UGc+UUc)=I _(Mc) +O_(CBc)(1−(GGc+(GGmr+GGcr)GUc/(GGmr+GGcr+GGr)+GGcr+UGc+UUc)/(GGc+GUc+GGcr+UGc+UUc)).  (206)

Using Equations (134), (144), (147), (149), (158), (161), (184), (185),(186), (187), (191) and (197) in Equation (183), one obtains:P≅(I _(ARc)/(GGc+GGm+GGcr+GGmr+GGr+OOn))(OGn−GOn−UGc−UGm+GUc+GUm))C_(R)+((Y_(Cc)−1)(GGc+(GGmr+GGcr)GUc/(GGmr+GGcr+GGr)+GGcr+UGc+UUc)/(GGc+GUc+GGcr+UGc+UUc))(1−(GGc+GUc+GGcr+(GGmr+GGcr)UGc/(GGmr+GGcr+GGr)+UUc)/(GGc+(GGmr+GGcr)GUc/(GGmr+GGcr+GGr)+GGcr+UGc+UUc))I_(Cc)(C _(M) +C _(MI))+((1−(1−Y_(Mc))(GGm+GUm+GGmr+(GGcr+GGmr)UGm/(GGcr+GGmr+GGr)+UUm)/(GGm+GUm+GGmr+UGm+UUm))(1−(1−Y_(Cc))(GGc+GUc+GGcr+(GGmr+GGcr)UGc/(GGmr+GGcr+GGr)+UUc)/(GGc+GUc+GGcr+UGc+UUc))−(1−(1−Y_(Mc))(GGm+(GGcr+GGmr)GUm/(GGcr+GGmr+GGr)+GGmr+UGm+UUm)/(GGm+GUm+GGmr+UGm+UUm))(1−(1−Y_(Cc))(GGc+(GGmr+GGcr)GUc/(GGmr+GGcr+GGr)+GGcr+UGc+UUc)/(GGc+GUc+GGcr+UGc+UUc)))P_(VALUE) I _(Cc).  (207)

The analysis described above is applicable to a production line modelthat does not utilize the optional cell and module repair stages 214 and216. However, it should be appreciated that the analysis described abovecan be adapted for a production line model that does utilize theoptional cell and model repair stages 214 and 216, while still fallingwithin the scope of the present invention. Further, if the optional celland module repair stages 214 and 216 are used, but the cell and modulerepair rates are so low as to not make a significant contribution to theyield rates, then the above-described analysis may be applied.

VIII. Threshold Optimization with No Assumption about Defects

The threshold optimization methodology described above is based on theassumption that the under-killed defects are the only dominant cause ofbad panels at cell and module inspections. Threshold optimization canalso be done without the assumption that the under-killed defects arethe only dominant cause of the bad panels at cell and moduleinspections.

FIG. 10 is a flow chart showing how profit maximization for the TFT-LCDproduction line can be achieved by optimization of the thresholdingparameters. The process begins at step 1000, and proceeds to step 1005,where the TFT-array panels are tested, at the array test stage 202, byTFT-array test equipment. The testing is done with “proto thresholding”parameters, which are tighter than the primary thresholding parametersof the primary test recipe. The generated proto defects (PD) fileidentifies more defective pixels than the normal production defects filegenerated by the primary thresholding. At step 1005, the primarythresholding parameters are set as “screen thresholding parameters”(Pth).

Next, at step 1010, initial defect sorting is performed for the PD file,in accordance with the flow chart of FIG. 11, in which primarythresholding parameters are applied to the proto defects file as screenthresholding parameters (Pth) to screen the PD file and generate ascreened defects (SD) file that is identical to the normal defects filegenerated by the primary thresholding.

Referring to FIG. 11, the initial defect sorting process starts at step1100, and proceeds to step 1105, where the screened defects (SD) file isgenerated by using screen thresholding, which screens the PD file byless stringent thresholding parameters than proto thresholdingparameters. Then, at step 1110, the SD is reviewed and the panels thatare visually confirmed as defective are repaired. The SD that has beenrepaired is noted as SDrp and is divided into two groups as follows: (1)Successfully repaired pixel (noted as Well)—no defect observed at laterinspections; and (2) Still defective due to improper repair: The defectis observed at either cell inspection (noted as CSDrp) or moduleinspection (noted as MSDrp).

An SD that has not been repaired is noted as SDnr and is divided intotwo groups as follows: (1) Over-kill at array test (noted as

)—no defect observed at later inspections; and (2) Defect due toimproper visual judge—Defect observed at either cell inspection (notedas CSDnr) or module inspection (noted as MSDnr).

Next, at step 1115, cell inspection confirms the defects reported beforeand changes the notation as follows:

 PD→CPD SDrp→CSDrp SDnr→CSDnr.

In addition, cell inspection detects new defects (noted as CND): ND→CND.

Then, at step 1120, module inspection confirms the defects reportedbefore and changes the notation as follows:PD→MPD SDrp→MSDrp SDnr→MSDnr.Also, module inspection detects new defects (noted as MND): ND→MND.

If the cell defects are repaired after the cell inspection, thenadditional sorting is done as follows:

-   (1) Module inspection confirms the defects reported by cell    inspection and changes the notation as follows:    CPD→MCPD CSDrp→MCSDrp CSDnr→MCSDnr CND∩MCND; and-   (2) Module inspection confirms the success of repair action done    after cell inspection, and changes the notation as follows:    CPD→RMCPD CSDrp→RMCSDrp CSDnr→RMCSDnr CND→RMCND

The process then ends at step 1125.

Referring back to FIG. 10, the result of the initial defect sortingshown in FIG. 11 is calculated at step 1015 as follows:Cell defect(T _(CD))=CPD+CSDrp+CSDnr+CND;  (208) Module defect(T _(MD))=MPD+MSDrp+MSDnr+MND; and  (209)Over-kill(

)=SDnr−(CSDnr+MSDnr).  (210)

After initial defect sorting, the screen thresholding parameters arescanned through the primary thresholding parameters in each zone, sothat they can be either tighter or looser than the primary thresholdingparameters, but not tighter than the proto thresholding parameters.

Whenever any of the screen thresholding parameters changes its value,defect resorting is done (step 1020) by applying the new parameter tothe PD file to determine the effects of the changed parameter. Next, atstep 1025, the benefit of the defect resorting is calculated. Theprocess then proceeds to step 1030, where a decision is made as towhether to continue scanning Pth, whose span is set by the user aroundprimary thresholding parameters with a restriction that Pth does notbecome tighter than the proto thresholding. If it is decided to continuescanning Pth, the process jumps to step 1050. Otherwise, the processcontinues to step 1035.

At step 1035, the optimum screen thresholding parameters (Pth) is chosenamong all the screen thresholding parameters evaluated and its benefitis determined. Next, at step 1040, a decision is made as to whether totry additional screen thresholding parameters based on the benefitdetermined at step 1035. If it is decided to try additional screenthresholding parameters, the process proceeds to step 1050. Otherwise,the process ends at step 1045.

At step 1050, the screen thresholding parameters are updated, and theprocess jumps back to step 1020.

FIG. 12 is a flow chart showing the method used for defect resorting(step 1020 of FIG. 10). The process starts at step 1200, and proceeds tostep 1205, where it is determined if the screen thresholding is equalto, tighter than, or looser than the primary thresholding. If the screenthresholding is looser than the primary thresholding, then the processjumps to step 1220. If the screen thresholding is equal to the primarythresholding, then the process jumps to step 1230, where the processends.

If the screen thresholding is tighter than the primary thresholding,then the process proceeds to step 1210, where a new screened defects(SD′) file is generated by using tighter screen thresholding. Tighterscreen thresholding decreases the number of PD, increases the number ofSD, and decreases the number of CPD and MPD compared to those of primarythresholding. The portion of decrease in the total cell or moduledefects is given by Rwell, which is defined as the number of wellrepaired pixel divided by the number of real defects that the repairoperator reviews and is expressed as (SDrp−CSDrp−MSDrp)/(SD−

), based on the assumption that the repair rate is maintained asconstant.

At step 1215, the change in CPD (ΔCPD), the change in MPD (ΔMPD) and thechange in SD (ΔSD) are calculated. The amount of increase of over-killeddefects is given by subtracting the increase of real defect detection,(ΔCPD+ΔMPD), from the increase of screened defects, ΔSD. Thus, when thescanned thresholding parameters are tighter than the primarythresholding parameters, the cell and module defects and over-killdefects are as follows:T′ _(CD) =CPD+CSDrp+CSDnr+CND−ΔCPD(SDrp−CSDrp−MSDrp)/(SD−);  (211)T′ _(MD) =MPD+MSDrp+MSDnr+MND−ΔMPD(SDrp−CSDrp−MSDrp)/(SD−); and  (212)′=SDnr−(CSDnr+MSDnr)+ΔSD−(ΔCPD+ΔMPD).  (213)

Other parameters can be obtained in a similar way as follows:Cell under-kill, CPD′=CPD−ΔCPD;  (214)CSD′rp=CSDrp+(ΔCPD+ΔMPD)CSDrp/(SD−);  (215)CSD′nr=CSDnr+(ΔCPD+ΔMPD)CSDnr/(SD−);  (216)Module under-kill, MPD′=MPD−ΔMPD;  (217)MSD′rp=MSDrp+(ΔCPD+ΔMPD)MSDrp/(SD−);  (218)MSD′nr=MSDnr+(ΔCPD+ΔMPD)MSDnr/(SD−);  (219)MCPD′=MCPD−ΔCPD;  (220)MCSD′rp=MCSDrp+(ΔCPD+ΔMPD)MCSDrp/(SD−); and  (221)MCSD′nr=MCSDnr+(ΔCPD+ΔMPD)MCSDnr/(SD−).  (222)

From Equations (208) and (211), the change in total cell defects(ε_(TCD)) due to tighter thresholding parameters is given by:ε_(TCD) =T _(CD) −T′ _(CD) =ΔCPD(SDrp−CSDrp−MSDrp)/(SD−).  (223)

From Equations (209) and (212), the change in total module defects(ε_(TMD)) due to tighter thresholding parameters is given by:ε_(TMD) =T _(MD) −T′ _(MD) =ΔMPD(SDrp−CSDrp−MSDrp)/(SD−).  (224)

From Equations (210) and (213), the change in over-kill defects (Δ

) due to tighter thresholding parameters is given by:Δ

=

−

′=ΔCPD+ΔMPD−ΔSD.  (225)

From Equations (214) and (217), the change in under-kill defects (ΔU)due to tighter thresholding parameters is given by:ΔU=U−U′=(CPD+MPD)−(CPD′+MPD′)=(CPD+MPD)−(CPD−ΔCPD+MPD−ΔMPD)=ΔCPD+ΔMPD.  (226)

From Equations (170), (171), (176), (177), (208), (209), (211), and(212), one obtains:Y′ _(C)=1−(1−Y_(C))(CPD+CSDrp+CSDnr+CND−ΔCPD(SDrp−CSDrp−MSDrp)/(SD−))/(CPD+CSDrp+CSDnr+CND);  (227)E _(YC) ≡Y′ _(C) −Y _(C)=(1−Y_(C))(1−(CPD+CSDrp+CSDnr+CND−ΔCPD(SDrp−CSDrp−MSDrp)/(SD−))/(CPD+CSDrp+CSDnr+CND));  (228) Y′ _(M)=1−(1−Y_(M))(MPD+MSDrp+MSDnr+MND−ΔMPD(SDrp−CSDrp−MSDrp)/(SD−))/(MPD+MSDrp+MSDnr+MND);and  (229)E _(YM) ≡Y′ _(M) −Y _(M)=(1−Y_(M))(1−(MPD+MSDrp+MSDnr+MND−ΔMPD(SDrp−CSDrp−MSDrp)/(SD−))/(MPD+MSDrp+MSDnr+MND)).  (230)

From Equations (94), (179), (208), (209), (211), (212), (225), and(226), one can obtain the expression for the profit increase from usingthe tighter thresholding parameters:P≅γΔSD C _(R)+(Y_(C)−1)(1−(CPD+CSDrp+CSDnr+CND−ΔCPD(SDrp−CSDrp−MSDrp)/(SD−))/(CPD+CSDrp+CSDnr+CND))I_(C)(C _(M) +C _(MI))+((1−(1−Y _(M))(MPD+MSDrp+MSDnr+MND−ΔMPD(SDrp−CSDrp−MSDrp)/(SD−))/(MPD+MSDrp+MSDnr+MND))(1−(1−Y_(C))(CPD+CSDrp+CSDnr+CND−ΔCPD(SDrp−CSDrp−MSDrp)/(SD−))/(CPD+CSDrp+CSDnr+CND))−Y_(M) Y _(C))P _(VALUE) I _(C).  (231)

The value of γ can be obtained with the assumption that O_(ATB) is verysmall compared with other parameters, as will now be described. FromEquations (91), (92), (93), (210) and (226), one obtains:I _(AR)=γ(R+−U)−O _(ATB)≅γ(R+−U)=γ((CPD+MPD+SD−)+

−(CPD+MPD))=γSD,  (232)where R is the number of real defects before repair, and is given by:R=CPD+MPD+SD−.  (233)Thus, from Equation (232), one obtains: γ=I _(AR) /SD.  (234)

From Equations (231) and (234), one obtains:P≅−ΔSD C _(R) I _(AR) /SD+(Y_(C)−1)(1−(CPD+CSDrp+CSDnr+CND−ΔCPD(SDrp−CSDrp−MSDrp)/(SD−))/(CPD+CSDrp+CSDnr+CND))I_(C)(C _(M) +C _(MI))+((1−(1−Y _(M))(MPD+MSDrp+MSDnr+MND−ΔMPD(SDrp−CSDrp−MSDrp)/(SD−))/(MPD+MSDrp+MSDnr+MND))(1−(1−Y_(C))(CPD+CSDrp+CSDnr+CND−ΔCPD(SDrp−CSDrp−MSDrp)/(SD−))/(CPD+CSDrp+CSDnr+CND))−Y_(M) Y _(C))P _(VALUE) I _(C).  (235)The values of Y_(C), Y_(M), I_(AR), and I_(C) can be obtained from thesample production runs using the primary thresholding parameters.

The use of looser screen thresholding parameters decreases the number ofSD and successfully repaired pixels, increases the number of PD, andincreases the number of CPD and MPD, compared to using the primarythresholding parameters. In order to analyze the effects of looserscreen thresholding parameters, the results of the primary thresholdingparameters, given by Equations (208) and (209), are expressed in adifferent format as follows:T _(CD) =CPD+CSDrp+CSDnr+CND=CPD+CSD′rp+CSD′nr+ΔCSDrp+ΔCSDnr+CND;and  (236)T _(MD) =MPD+MSDrp+MSDnr+MND=MPD+MSD′rp+MSD′nr+ΔMSDrp+ΔMSDnr+MND,  (237)where ΔCSDrp indicates the number of CSDrp that are converted to CPD andis obtained by (CSDrp−CSD′rp), ΔCSDnr indicates the number of CSDnr thatare converted to CPD and is obtained by (CSDnr−CSD′nr), ΔMSDrp indicatesthe number of MSDrp that are converted to MPD and is obtained by(MSDrp−MSD′rp), and ΔMSDnr indicates the number of MSDnr that areconverted to MPD and is obtained by (MSDnr−MSD′nr).

The increase in the cell or module defects, which is due to thereduction of the number of successfully repaired pixels, is given by Rwcand Rwm, respectively, based on the assumption that the reverse rate ofunder-kill defects from the successfully repaired pixels remainsconstant, and is determined by the following ratios of under-killdefects for the primary thresholding parameters:Rwc=Number of cell under-kill defects/Total number of under-killdefects=CPD/(CPD+MPD); and  (238)Rwm=Number of module under-kill defects/Total number of under-killdefects=MPD/(CPD+MPD).  (239)

Thus, when the scanned thresholding parameters are looser than theprimary thresholding parameters, the cell and module defects are givenas follows (from Equations (208), (209), (238), and (239)):T′ _(CD) =T _(CD) +ΔWell Rwc=CPD+CSDrp+CSDnr+CND+ΔWell CPD/(CPD+MPD);and  (240)T′ _(MD) =T _(MD) +ΔWell Rwm=MPD+MSDrp+MSDnr+MND+ΔWellMPD/(CPD+MPD),  (241)where ΔWell is the portion of successfully repaired pixels with primarythresholding that would not have been detected with looser thresholding,and become either cell or module under-kill defects. With looserthresholding, the number of over-killed defects is decreased becausesome portion of

(Δ

) would not have been reported as defects. From FIG. 11, one obtains:SD=SDrp+SDnr; and  (242)SDrp=CSDrp+MSDrp+Well,  (243)where Well is the number of successfully repaired defects. FromEquations (210), (242) and (243), one obtains the following expressionfor Δ

:Δ

=

−

′=(SDnr−(CSDnr+MSDnr))−(SD′nr−(CSD′nr+MSD′nr))=(SD−SDrp−(CSDnr+MSDnr))−(SD′−SD′rp−(CSD′nr+MSD′nr))=(SD−(CSDrp+MSDrp+Well)−(CSDnr+MSDnr))−(SD′−(CSD′rp+MSD′rp+W′ell)−(CSD′nr+MSD′nr))=(SD−SD′)−(CSDrp−CSD′rp+MSDrp−MSD′rp+Well−W′ell)−(CSDnr−CSD′nr+MSDnr−MSD′nr)=ΔSD−ΔCSDrp−ΔCSDnr−ΔMSDrp−ΔMSDnr−Δwell.  (244)

Other parameters can be obtained by similar way as follows:Cell under-kill, CPD′=CPD+ΔCSDrp+ΔCSDnr+ΔWell Rwc;  (245)CSD′rp=CSDrp−ΔCSDrp;  (246)CSD′nr=CSDnr−ΔCSDnr;  (247) Module under-kill, MPD′=MPD+ΔMSDrp+ΔMSDnr+ΔWell Rwm;  (248)MSD′rp=MSDrp−ΔMSDrp;  (249)MSD′nr=MSDnr−ΔMSDnr;  (250)MCPD′=MCPD+ΔCSDrp+ΔCSDnr+ΔWell Rwc;  (251)MCSD′rp=MCSDrp−ΔMCSDrp; and  (252)MCSD′nr=MCSDnr−ΔMCSDnr.  (253)

From Equations (236) and (240), the effect of looser thresholdingparameters over the primary thresholding parameters on the total celldefects (ε_(TCD)) is obtained by:ε_(TCD) =T _(CD) −T′ _(CD) =−ΔWell Rwc=−ΔWell CPD/(CPD+MPD).  (254)

From Equations (237) and (241), the effect of looser thresholdingparameters over the primary thresholding parameters for the total moduledefects (ε_(TMD)) is obtained byε_(TMD) =T _(MD) −T′ _(MD) =−ΔWell Rwm=−ΔWell MPD/(CPD+MPD).  (255)

From Equations (238), (239), (245) and (248), the effect of looserthresholding parameters over the primary thresholding parameters for theunder-kill defects (ΔU) is obtained by:ΔU=U−U′=(CPD+MPD)−(CPD′+MPD′)=(CPD+MPD)−(CPD+ΔCSDrp+ΔCSDnr+ΔWellRwc+MPD+ΔMSDrp+ΔMSDnr+ΔWell Rwm)=−(ΔCSDrp+ΔCSDnr+ΔWell Rwc+ΔMSDrp+ΔMSDnr+ΔWellRwm)=−(ΔCSDrp+ΔCSDnr+ΔWell+ΔMSDrp+ΔMSDnr).  (256)

From Equations (170), (171), (176), (177), (236), (237), (240) and(241), one obtains:Y′ _(C)=1−(1−Y _(C))(CPD+CSDrp+CSDnr+CND+ΔWellCPD/(CPD+MPD))/(CPD+CSDrp+CSDnr+CND);  (257)E _(YC) ≡Y′ _(C) −Y _(C)=(1−Y _(C))(1−(CPD+CSDrp+CSDnr+CND+ΔWellCPD/(CPD+MPD))/(CPD+CSDrp+CSDnr+CND));  (258)Y′ _(M)=1−(1−Y _(M))(MPD+MSDrp+MSDnr+MND+ΔWellMPD/(CPD+MPD))/(MPD+MSDrp+MSDnr+MND); and  (259)E _(YM) ≡Y′ _(M) −Y _(M)=(1−Y _(M))(1−(MPD+MSDrp+MSDnr+MND+ΔWellMPD/(CPD+MPD))/(MPD+MSDrp+MSDnr+MND)).  (260)

From Equations (244) and (256), one obtains:Δ−ΔU=ΔSD.  (261)

From Equations (94), (179), (234), (236), (237), (240), (241) and (261),one can obtain the expression for the profit increase resulting from thelooser thresholding parameters as follows:P≅ΔSD C _(R) I _(AR) /SD+(Y _(C)−1)(1−(CPD+CSDrp+CSDnr+CND+ΔWellCPD/(CPD+MPD))/(CPD+CSDrp+CSDnr+CND))I _(C)(C _(M) +C _(MI))+((1−(1−Y_(M))(MPD+MSDrp+MSDnr+MND+ΔWell MPD/(CPD+MPD))/(MPD+MSDrp+MSDnr+MND))(1−(1−Y _(C))(CPD+CSDrp+CSDnr+CND+ΔWellCPD/(CPD+MPD))/(CPD+CSDrp+CSDnr+CND))−Y _(M) Y _(C))P _(VALUE) I_(C).  (262)

If the cell defects are repaired after the cell inspection stage 208,then the successful rate of cell repair, Rcell, can be obtained fromFIG. 11 as follows:Rcell=(RMCPD+RMCSDrp+RMCSDnr+RMCND)/(CPD+CSDrp+CSDnr+CND).  (263)

Once the profit maximization has been achieved for one screenthresholding parameter, then another profit maximization process isperformed for another screen thresholding parameter in its scanningzone. This profit maximization process is repeated for all remainingscreen thresholding parameters. The data for profit maximization shouldbe obtained from the entire sample production runs, and the optimumscreen thresholding parameters are preferably chosen that will maximizethe profit for the entire production run.

The analysis described above is applicable to a production line modelthat does not utilize the optional cell and module repair stages 214 and216. However, it should be appreciated that the analysis described abovecan be adapted for a production line model that does utilize theoptional cell and model repair stages 214 and 216, while still fallingwithin the scope of the present invention. Further, if the optional celland module repair stages 214 and 216 are used, but the cell and modulerepair rates are so low as to not make a significant contribution to theyield rates, then the above-described analysis may be applied.

IX. Profit Maximization of Both Primary and New Test

Profit maximization for both new and primary test recipes using the samesample production runs will now be described. FIGS. 13A-13D illustrate aflow chart for profit maximization of new and primary test recipes.

The process starts at step 1300, and proceeds to step 1302, where sampleproduction runs are tested by the TFT-array test equipment at the arraytest stage (AT) with a primary distribution function test recipe andprimary thresholding parameters (θ_(PRIME)). The test result is labeledprimary defect files (DF_(PRIME)). Then, the same sample production runsare retested with the primary distribution function test recipe and1^(st) proto thresholding, and the test result is labeled “1^(st) PDfile.” Then, the same sample production runs are retested with a newdistribution function test recipe and 2^(nd) proto thresholding, and thetest result is called “2^(nd) PD file.”

Then, at step 1304, thresholding for the new distribution function testrecipe (θ_(NEW)), which is looser than the 2^(nd) proto thresholding, isapplied to the 2^(nd) PD file to generate defect files labeled DF_(NEW).Next, at step 1306, the sample production runs proceed to the TFT-arrayrepair stage 204 and, as described above in Section VII, only the pixelscommonly reported as defects in DF_(PRIME) and DF_(NEW) are reviewed bythe operator of the TFT-array repair equipment, and the operatorattempts to repair the pixels when the defects are visually confirmed.The sample production runs then proceed to next process stage, which isassumed to have not include the optional cell and module repair stages214 and 216.

For evaluation of new distribution function test recipe, as describedabove in Section VII, the defects reported in DF_(PRIME) and DF_(NEW)are sorted out based on the repair actions performed on the defects andthe results of cell and module inspections. Then, at step 1308, theeffect of the new distribution function test recipe is calculated, asdescribed above in Section VII.

At step 1310, it is decided whether to continue tuning θ_(NEW), whosespan is set by the user around the starting θ_(NEW) in step 1304 with arestriction that θ_(NEW) does not become tighter than the 2^(nd) protothresholding. If the decision is made to not continue θ_(NEW) scanning,then the process jumps to step 1326 (FIG. 13C). Otherwise, the processcontinues to step 1312.

At step 1312, θ_(NEW) is updated and applied to the 2^(nd) PD file togenerate an SD′_(NEW) file. Next, at step 1314, it is determined ifθ_(NEW) has been updated to tighter or looser thresholding. If θ_(NEW)is updated to tighter thresholding, then the process proceeds to step1318, where the values of GUc, GUm, OGn, UUc, UUm and GGn decrease byΔGUc, ΔGUm, ΔOGn, ΔUUc, ΔUUm, and ΔGGn, respectively, because theSD′_(NEW) files report these as additional defects. FIG. 14 is a tableshowing how the defect sorting result is modified by the additionaldefects. In the table of FIG. 14, GGcr is increased by (1−Nc) ΔGUc, GGmrby (1−Nm) ΔGUm, and GGr by Nc ΔGUc+Nm ΔGUm, based on the sameassumptions used in the table of FIG. 8 above.

If θ_(NEW) is updated to looser thresholding, the process proceeds tostep 1316, where the values of GGc, GGm, OOn, GGcr, GGmr, GGr, UGc, UGm,and GOn decrease by ΔGGc, ΔGGm, ΔOOn, ΔGGcr, ΔGGmr, ΔGGr, ΔUGc, ΔUGm,and ΔGOn, respectively, because these are included in the 2^(nd) PDfiles, but not included in the SD′_(NEW) files as defects. FIG. 15 is atable showing how the defect sorting result is modified by the decrementof reported defects in the SD′_(NEW). In the table of FIG. 15, GUc isincreased by ΔGGc+ΔGGcr+ΔGGr GUc/(GUc+GUm) and GUm is increased byΔGGm+ΔGGmr+ΔGGr GUm/(GUc+GUm), based on the assumption that the reverserate to GUc or GUm from the successfully repaired pixels when θ_(NEW)becomes looser is maintained constant and is determined by the ratio ofGUc and GUm for the starting θ_(NEW).

Once the parameters are updated, as shown in the tables of FIG. 14 or15, then the effect of the new θ_(NEW) can be obtained by using theanalysis of Section VII. Therefore, profit maximization can be achievedby taking the maximum value of P while θ_(NEW) is scanned through thestarting θ_(NEW) in its scanning zone. Once the profit maximization hasbeen achieved for one θ_(NEW) parameter, then another profitmaximization process is performed for another θ_(NEW) parameter in itsscanning zone. This profit maximization process is repeated for all theremaining θ_(NEW) parameters, and is carried out by steps 1312-1324. Thedata for profit maximization is preferably obtained from the entiresample production runs, and θ_(NEW) parameters are preferably chosenthat will maximize profits (P) for the entire production runs.

Once the θ_(NEW) parameters are chosen, the process continues to step1326, at which a decision is made as to whether to continue scanningprimary thresholding parameters (θ_(PRIME)), whose span is set by theuser around the starting θ_(PRIME) in step 1302 with a restriction thatθ_(PRIME) does not become tighter than the 1^(st) proto thresholding. Ifa decision is made to continue θ_(PRIME) scanning, then the processcontinues to step 1328, where θ_(PRIME) is applied to the 1^(st) PD fileto generate a defect file labeled SD_(PRIME) file. The parameters shownin FIG. 11 above must be defined for the profit maximization process forthe primary test recipe. Since only the pixels commonly reported asdefects in DF_(PRIME) and DF_(NEW) were reviewed by the operator of theTFT-array repair equipment, and the operator attempted to repair thepixels when the defects were visually confirmed, the table of FIG. 8needs to be used for the defect sorting table for the assumed scenarioof primary-test-only at the TFT-array test stage 202. By comparing thetable of FIG. 8 and FIG. 11, one can obtain the revised defect sortingtable in conjunction with the initial defect sorting of FIG. 11, for theassumed scenario of primary-test-only. This table is shown in FIG. 16.

The table of FIG. 16 is used in step 1330, to obtain the parameters ofFIG. 11. The expressions for CPD, MPD, CND, and MND are obtained asfollows:CPD=(UGc+UUc)∩PD _(PRIME)=(UGc+UUc)∩(1^(st) PD file∩{overscore (SD_(PRIME) )});  (264)MPD=(UGm+UUm)∩PD _(PRIME)=(UGm+UUm)∩(1^(st) PD file∩{overscore (SD_(PRIME) )});  (265)CND(UGc+UUc)−CPD; and  (266)MND(UGm+UUm)−MPD.  (267)Then, Equations (208) to (210) can be used to calculate the effect ofthe primary-test-only.

At step 1332, for tuning of the primary test recipe, θ_(PRIME) isupdated and applied to the 1^(st) PD file to generate the SD′_(PRIME)file. The process then proceeds to step 1334 (FIG. 13D), where it isdetermined if θ_(PRIME) has been updated to tighter or looserthresholding. If θ_(PRIME) is updated to tighter thresholding, then theprocess proceeds to step 1338, where the values of CPD and MPD decreaseby ΔCPD and ΔMPD, respectively, and the value of SD increases by ΔSD,because the SD′_(PRIME) files report additional defects of ΔSD. Theexpressions for ΔCPD, ΔMPD, and ΔSD are obtained as follows usingEquations (264) and (265):ΔCPD=CPD∩SD′ _(PRIME)=((UGc+UUc)∩PD _(PRIME))∩SD′ _(PRIME);  (268)ΔMPD=MPD∩SD′ _(PRIME)=((UGm+UUm)∩PD _(PRIME))∩SD′ _(PRIME); and  (269)ΔSD=SD′ _(PRIME) −SD _(PRIME).  (270)

If θ_(PRIME) is updated to looser thresholding, then the processproceeds to step 1336, where the values of CSDrp, CSDnr, MSDrp, MSDnr,Well, and SD decrease by ΔCSDrp, ΔCSDnr, ΔMSDrp, ΔMSDnr, ΔWell, and ΔSD,respectively, because the SD′_(PRIME) files do not report these asdefects. The expressions for ΔCSDrp, ΔCSDnr, ΔMSDrp, ΔMSDnr, ΔWell, andΔSD are obtained as follows using the table of FIG. 16:ΔCSDrp=CSDrp∩PD′ _(PRIME) =GGcr∩PD′ _(PRIME)+(1−Nc)(GUc∩PD′_(PRIME));  (271)ΔCSDnr=CSDnr∩PD′ _(PRIME) =GGc∩PD′ _(PRIME);  (272)ΔMSDrp=MSDrp∩PD′_(PRIME) =GGmr∩PD′ _(PRIME)+(1−Nm)(GUm∩PD′PRIME);  (273)ΔMSDnr=MSDnr∩PD′_(PRIME) =GGm∩PD′ _(PRIME);  (274)ΔWell=Well∩PD′ _(PRIME) =GGr∩PD′ _(PRIME) +Nc(Guc∩PD′_(PRIME))+Nm(Gum∩PD′ _(PRIME)); and  (275)ΔSD=SD _(PRIME) −SD′ _(PRIME),  (276)where PD′_(PRIME)=1^(st) PD file∩{overscore (SD′_(PRIME))}.

Once the parameters are updated using Equations (268) to (270) fortighter θ_(PRIME) and using Equations (271) to (276) for looserθ_(PRIME), then the effect of the new θ_(PRIME) can be obtained by usingthe analysis of Section VIII. Therefore, profit maximization can beachieved by taking the maximum value of P while θ_(PRIME) is scannedthrough the starting θ_(PRIME) in its scanning zone. Once the profitmaximization has been achieved for one θ_(PRIME) parameter, then anotherprofit maximization process is performed for another θ_(PRIME) parameterin its scanning zone. This profit maximization process is repeated forall the remained θ_(PRIME) parameters, and is carried out by steps1332-1344. The data for profit maximization should be obtained from theentire sample production runs and θ_(PRIME) parameters are preferablychosen that maximize the profit (P) for the entire production runs. Theprocess then ends at step 1346.

X. Dependence of Thresholding Parameters on Defect Probability

As discussed in Section III, when measuring TFT-array panels usingTFT-array test equipment, normal pixels have some voltage distributionaround a mean value, as shown in FIG. 3, mainly due to the noiseinvolved in measuring the pixel voltages. This causes some of the normalpixels with extreme noise magnitudes to be falsely reported as defects.The voltage distribution of defective pixels is not always distinct fromthat of normal pixels, and this causes some of the defective pixels togo through the TFT-array test undetected and become under-killeddefects.

In general, tighter thresholding allows less under-killed defects andmore over-killed defects, and looser thresholding allows moreunder-killed defects and less over-killed defects. Some defects exhibitvery small defect signals, meaning that their pixel voltages are veryclose to normal pixel voltages, and very tight thresholding is requiredto detect these kinds of defects however, very tight thresholdingresults in too many over-killed defects. An improved thresholding schemewill now be described that detects more defects, but only increasesover-killed defects by a negligibly small amount.

If multiple pixels in very close proximity have some deviation in theirpixel voltages from the normal pixel voltage, then tighter thresholdingthan is needed for an isolated defect should be applied to these pixels,because multiple defects in very close proximity are much more likely tocome from a single process abnormality that covers multiple pixels thanfrom multiple isolated defects in close proximity, as will now beexplained.

The probability of having the second isolated defect in the area ofA_(NEAR) near the first defect (PB_(NT)) is given by“PB_(NT)=A_(NEAR)/A_(TOTAL)”, where A_(TOTAL) is the total display areaof the TFT-array panel. The area covering two defects in close proximity(A_(NEAR)) is usually very small compared to A_(TOTAL). If A_(NEAR) isdefined by a 10 by 10 pixel array and A_(TOTAL) is 10⁶ pixels, thenPB_(NT)=10×10/10⁶=10⁻⁴.

If the probability of a single process abnormality covering two pixelsis comparable to that of the first isolated defect, then the probabilityof having two defects in very close proximity due to a single processabnormality is larger (on the order of about 10⁴ larger) than that dueto two isolated defects in close proximity. Therefore, the thresholdingshould be tighter for multiple defects in close proximity as the numberof defects in close proximity increases, because the probability ofhaving multiple defects in very close proximity due to a single processabnormality is increasingly larger on the order of about 10⁴ times thenumber of multiple defects than that due to multiple isolated defects inclose proximity.

Single process abnormalities involving a signal line, such as data,scanning, or common line, can cause multiple defects along the line. Theprobability of having multiple isolated defects in a linear form isextremely low, based on reasoning similar to that explained above. Thus,the thresholding for defects in a line should also be tighter than thenormal thresholding used for an isolated defect.

Process abnormalities can effect a relatively large area of the display,causing many isolated pixels over the relatively large area to havepixel voltages that are slightly deviated from the mean value of normalpixel voltages. Thus, tighter thresholding than that normally used fordetecting an isolated defect should be applied to those defectsscattered over the relatively large area, if the total number of defectsin the defined area exceeds some pre-defined critical number. Ingeneral, tighter thresholding should be applied to multiple defects ifthey are caused by certain single process abnormalities with higherprobability.

In some manufacturing lines, additional inspection equipment calledautomated optical inspection (AOI) equipment may also be used in the TFTarray process area to detect process abnormalities in the TFT-arraypanel. One of the difficulties of this type of inspection is that notevery process abnormality detected by the AOI equipment is related tofunctional defects in the TFT-LCD unit, even though the processabnormalities detected by AOI equipment end up causing functionaldefects with reasonably high probability. Thus tighter thresholdingshould be applied to the defects already detected as processabnormalities by the AOI equipment. One can correlate the thresholdingof the TFT-array test with the area of process abnormality detected bythe AOI equipment, so that tighter thresholding is used as the area ofprocess abnormality gets larger.

Therefore, in order to increase the defect detection efficiency, thefirst defect file should be generated by the tightest thresholding todetect all the potential defects. Then, the defect file is preferablyscreened by next tightest thresholding to detect the defects thatsatisfy the right criteria for that specific thresholding. Thisprocedure is preferably continued until all the different thresholdinglevels are applied to the potential defects.

XI. Sample Results

As discussed above, the profit of TFT-LCD manufacturing can be maximizedby optimizing the parameters of the TFT-array test. The profitmaximization is performed by finding the test parameters that strike theright balance between improvement of cell and module yields, andreducing the costs of the TFT-array repair process.

FIG. 17 is a plot showing an example of the distribution of normal 1700and defective 1710A and 1710B pixel voltages of a TFT-array panel, whichare used as the basis of parameter optimization. The distribution ofnormal pixel voltages 1700 can be represented by a statisticaldistribution function, because of the large number of pixels perTFT-array panel, and because of sensor's statistical measurementproperties. Thus, the distribution of normal pixel voltages 1700 can bewell represented by a normal distribution function. The distribution ofdefect pixel voltages 1710A and 1710B is not fixed, but is dependent onthe specific process problems. The distribution of defect pixel voltages1710A and 1710B is assumed to be constant between arbitrary values ofpixel voltages.

As discussed above, TFT-array test equipment uses thresholdingparameters to detect the defective pixels. Pixels are reported asdefects when their pixel voltages fall outside of the threshold region.If a normal pixel has its pixel voltage outside of the threshold region,then the normal pixel is wrongly reported as a defect and this kind ofpixel is called an over-killed defect. If a defective pixel has itspixel voltage within the threshold region, then the defective pixel iswrongly reported as a normal pixel, and this kind of pixel is called anunder-killed defect.

FIG. 18 is a plot showing the over-killed and under-killed defects asthe thresholding parameters are scanned, based on the distribution ofnormal and defect pixel voltages shown in FIG. 17.

FIG. 19 is a plot showing the differential effect of changing thresholdparameters for under-killed defects, as compared with the resultsobtained with the primary thresholding parameters, based on theunder-killed defects shown in FIG. 18.

FIG. 20 is a plot showing the differential effect of changing thresholdparameters on over-killed defects, as compared with the results obtainedwith the primary thresholding parameters, based on the over-killeddefects shown in FIG. 18.

FIG. 21 is a plot showing the differential effect of changing thresholdparameters on cell and module yields, as compared with the resultsobtained with the primary thresholding parameters, based on thedifferential under-killed defects shown in FIG. 19.

FIG. 22 is a plot showing the differential effect of changing thresholdparameters on total monetary benefit, as compared with the resultsobtained with the primary thresholding parameters, based on thedifferential effect on over-killed defects shown in FIG. 20 and thedifferential effect on cell and module yields shown in FIG. 21.

FIG. 23 is a plot showing the under-killed defects for different defectdensity values. The numbers in the legend indicate the multiplicationconstants applied to the starting defect density used in FIG. 17.

FIG. 24 is a plot showing the differential effect of changing thresholdparameters on the total monetary benefit for the defect densities usedin FIG. 23. The numbers in the legend indicate the multiplicationconstants applied to the starting defect density used in FIG. 17. Theprofit maximization can be achieved by taking the thresholdingparameters that yield the peak points of total monetary benefit, whilethe thresholding variables are scanned around the primary thresholdingparameters.

FIG. 25 is a plot showing how the profit improvement increases withincreasing defect density, based on the differential total monetarybenefit shown in FIG. 24. The alphabets in the legend indicate thedifferent scanning zones used in FIG. 24.

The foregoing embodiments and advantages are merely exemplary and arenot to be construed as limiting the present invention. The presentteaching can be readily applied to other types of apparatuses. Thedescription of the present invention is intended to be illustrative, andnot to limit the scope of the claims. Many alternatives, modifications,and variations will be apparent to those skilled in the art. In theclaims, means-plus-function clauses are intended to cover the structuresdescribed herein as performing the recited function and not onlystructural equivalents but also equivalent structures.

1. A method of determining thresholding parameters for a test recipethat will optimize a liquid crystal display (LCD) manufacturingparameter, wherein the test recipe comprises pixel driving signalsapplied to electrode array panels by an array test stage, and thethresholding parameters are used by the array test stage to identifygood and defective pixels in the electrode array panels based on pixelvoltage distributions generated in response to the pixel drivingsignals, the method comprising: (a) evaluating the LCD manufacturingparameter using thresholding parameters with current values; (b)evaluating the LCD manufacturing parameter while scanning the value of athresholding parameter from its current value and holding the values ofother thresholding parameters, if any, at current values; (c)identifying a new value for the scanned thresholding parameter thatresults in an optimized LCD manufacturing parameter, based on step (b);and (d) repeating steps (a)-(c) until all thresholding parameters havebeen scanned from their current values.
 2. The method of claim 1,wherein the test recipe generates positive polarity and negativepolarity pixel voltage distributions.
 3. The method of claim 2, whereinthe pixel voltage distributions generated by the pixel driving signalscomprise: a positive polarity normal pixel voltage distribution; apositive polarity defective pixel voltage distribution; a negativepolarity normal pixel voltage distribution; and a negative polaritydefective pixel voltage distribution.
 4. The method of claim 3, whereintwo thresholding parameters are used by the array test stage for each ofthe pixel voltage distributions.
 5. The method of claim 1, wherein theevaluation of the LCD manufacturing parameter is based on under-killedand over-killed defect parameters.
 6. The method of claim 1, wherein theLCD manufacturing parameter comprises an LCD yield.
 7. The method ofclaim 1, wherein the LCD manufacturing parameter comprises profit.
 8. Asystem for determining thresholding parameters for a test recipe thatwill optimize a liquid crystal display (LCD) manufacturing parameter,wherein the test recipe comprises pixel driving signals applied toelectrode array panels, comprising: an array test stage for applying thetest recipe to the electrode array panels, and for identifying good anddefective pixels in the electrode array panels based on the thresholdingparameters and the pixel voltage distributions generated in response tothe pixel driving signals; and a processor for: (a) evaluating the LCDmanufacturing parameter using thresholding parameters with currentvalues; (b) evaluating the LCD manufacturing parameter while scanningthe value of a thresholding parameter from its current value and holdingthe values of other thresholding parameters, if any, at current values;(c) identifying a new value for the scanned thresholding parameter thatresults in an optimized LCD manufacturing parameter, based on step (b);and (d) repeating steps (a)-(c) until all thresholding parameters havebeen scanned from their current values.
 9. The system of claim 8,wherein the test recipe generates positive polarity and negativepolarity pixel voltage distributions.
 10. The system of claim 9, whereinthe pixel voltage distributions generated by the pixel driving signalscomprise: a positive polarity normal pixel voltage distribution; apositive polarity defective pixel voltage distribution; a negativepolarity normal pixel voltage distribution; and a negative polaritydefective pixel voltage distribution.
 11. The system of claim 10,wherein two thresholding parameters are used by the array test stage foreach of the pixel voltage distributions.
 12. The system of claim 8,wherein the evaluation of the LCD manufacturing parameter is based onunder-killed and over-killed defect parameters.
 13. The system of claim8, wherein the LCD manufacturing parameter comprises an LCD yield. 14.The system of claim 8, wherein the LCD manufacturing parameter comprisesprofit.
 15. An article of manufacture, comprising: a computer usablemedium having computer readable program code embodied therein fordetermining thresholding parameters for a test recipe that will optimizea liquid crystal display (LCD) manufacturing parameter, wherein the testrecipe comprises pixel driving signals applied to electrode array panelsby an array test stage, and the thresholding parameters are used by thearray test stage to identify good and defective pixels in the electrodearray panels based on pixel voltage distributions generated in responseto the pixel driving signals, the computer readable program code in thearticle of manufacture causing a computer to: (a) evaluate the LCDmanufacturing parameter using thresholding parameters with currentvalues; (b) evaluate the LCD manufacturing parameter while scanning thevalue of a thresholding parameter from its current value and holding thevalues of other thresholding parameters, if any, at current values; and(c) identify a new value for the scanned thresholding parameter thatresults in an optimized LCD manufacturing parameter, based on step (b);and (d) repeat steps (a)-(c) until all thresholding parameters have beenscanned from their current values.
 16. The article of manufacture ofclaim 15, wherein the computer readable program code causes a computerto evaluate the LCD manufacturing parameter based on under-killed andover-killed defect parameters.
 17. A program storage device readable bya machine, tangibly embodying a program of instructions executable bythe machine to perform method steps for determining thresholdingparameters for a test recipe that will optimize a liquid crystal display(LCD) manufacturing parameter, wherein the test recipe comprises pixeldriving signals applied to electrode array panels by an array teststage, and the thresholding parameters are used by the array test stageto identify good and defective pixels in the electrode array panelsbased on pixel voltage distributions generated in response to the pixeldriving signals, the method comprising: (a) evaluating the LCDmanufacturing parameter using thresholding parameters with currentvalues; (b) evaluating the LCD manufacturing parameter while scanningthe value of a thresholding parameter from its current value and holdingthe values of other thresholding parameters, if any, at current values;(c) identifying a new value for the scanned thresholding parameter thatresults in an optimized LCD manufacturing parameter, based on step (b));and (d) repeating steps (a)-(c) until all thresholding parameters havebeen scanned from their current values.
 18. The program storage deviceof claim 17, wherein the test recipe generates positive polarity andnegative polarity pixel voltage distributions.
 19. The program storagedevice of claim 18, wherein the pixel voltage distributions generated bythe pixel driving signals comprise: a positive polarity normal pixelvoltage distribution; a positive polarity defective pixel voltagedistribution; a negative polarity normal pixel voltage distribution; anda negative polarity defective pixel voltage distribution.
 20. Theprogram storage device of claim 19, wherein two thresholding parametersare used by the array test stage for each of the pixel voltagedistributions.
 21. The program storage device of claim 17, wherein theevaluation of the LCD manufacturing parameter is based on under-killedand over-killed defect parameters.
 22. The program storage device ofclaim 17, wherein the LCD manufacturing parameter comprises an LCDyield.
 23. The program storage device of claim 17, wherein the LCDmanufacturing parameter comprises profit.